Finite Group Databasebeta

← C11×#24358 #14601551

Subgroups — C11×#24358 #14601551

Order 2816.

1598 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×SD16C211yesmaximal, characteristic
2C2×C11×#461C212yesmaximal, complemented
3C2×C11×#450C211yesmaximal, characteristic
4C11×#2434C211yesmaximal, characteristic, complemented
5D4×C11×C22⋊C4C211yesmaximal, characteristic
6C11×#2055C212yesmaximal, complemented
7C11×#2013C212yesmaximal, complemented
8C11×#1892C211yesmaximal, characteristic, complemented
9C11×#1877C212yesmaximal, complemented
10C11×#1850C211yesmaximal, characteristic, complemented
11C11×#1787C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C23×D4×C11C2211yescharacteristic
14C22×C11×SD16—24no—
15C22×C11×SD16—28no—
16C22×C11×SD16C2211yescharacteristic
17C22×C11×SD16C2212yes—
18C22×C11×SD16C2212yes—
19C22×C11×SD16C2211yescharacteristic
20C23×C8×C11C2211yescharacteristic
21C2×C11×C4⋊Q8C2212yescomplemented
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C4×D4×C11C2212yes—
24C22×C11×C22⋊C4—21no—
25C11×#461—28no—
26C11×#450—24no—
27C2×C11×C4⋊C8C2212yescomplemented
28C2×C11×#103C2212yescomplemented
29C2×C11×#103C2212yescomplemented
30C2×C11×#103C2212yescomplemented
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×C22⋊C8C2211yescharacteristic
34C11×#395—22no—
35C11×#391C2212yescomplemented
36C11×#390C2212yes—
37C11×#386—22no—
38C11×#385—21no—
39C11×#385—21no—
40C11×#380C2211yescharacteristic
41C11×#379—21no—
42C4×C11×C22⋊C4C2211yescharacteristic
43C11×#340C2212yescomplemented
44C11×#336C2212yescomplemented
45C25×C11—21no—
46C22×Q8×C11—21no—
47C22×Q8×C11—24no—
48C22×Q8×C11—22no—
49C22×Q8×C11—22no—
50C22×Q8×C11—42no—
51C22×Q8×C11C2311yescharacteristic
52C22×Q8×C11C2312yes—
53C22×D4×C11—24no—
54C22×D4×C11—21no—
55C22×D4×C11—22no—
56C22×D4×C11—42no—
57C22×D4×C11D414yes—
58C22×D4×C11C2311yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11—22no—
62C23×C4×C11C2311yescharacteristic
63C2×C11×SD16—232no—
64C2×C11×SD16—24no—
65C2×C11×SD16—24no—
66C2×C11×SD16—24no—
67C2×C11×SD16—24no—
68C2×C11×SD16—22no—
69C2×C11×SD16—22no—
70C2×C11×SD16—24no—
71C2×C11×SD16—24no—
72C2×C11×SD16—42no—
73C2×C11×SD16D418yes—
74C22×C8×C11—22no—
75C22×C8×C11—24no—
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2312yes—
79C11×C4⋊Q8—24no—
80C11×C4⋊Q8—42no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—22no—
83C4×D4×C11—24no—
84C4×D4×C11—42no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—44no—
96C2×C11×C22⋊C4D411yescharacteristic
97C2×C11×C22⋊C4D411yescharacteristic
98C2×C42×C11C2312yes—
99C11×C4⋊C8—24no—
100C11×#103—24no—
101C11×#103—24no—
102C11×#103—42no—
103C11×#102—22no—
104C11×#102—22no—
105C11×C22⋊C8—22no—
106C11×#95—21no—
107C11×#95—22no—
108C11×#95—22no—
109C11×#95D412yes—
110#24358C1111yesmaximal, characteristic, direct product factor, Sylow
111C24×C11—21no—
112C24×C11—21no—
113C24×C11—24no—
114C24×C11—44no—
115C24×C11—42no—
116C24×C11—42no—
117C24×C11—82no—
118C24×C11C2×D411yescharacteristic
119C2×Q8×C11—22no—
120C2×Q8×C11—28no—
121C2×Q8×C11—22no—
122C2×Q8×C11—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11—21no—
125C2×Q8×C11—22no—
126C2×Q8×C11—21no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—44no—
130C2×Q8×C11—48no—
131C2×Q8×C11—44no—
132C2×Q8×C11—42no—
133C2×Q8×C11C2×D414yes—
134C2×D4×C11—28no—
135C2×D4×C11—24no—
136C2×D4×C11—22no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—44no—
142C2×D4×C11—48no—
143C2×D4×C11—44no—
144C2×D4×C11C2×D412yes—
145C2×D4×C11C2×D412yes—
146C2×D4×C11C2×D414yes—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11—21no—
153C22×C4×C11—44no—
154C22×C4×C11—44no—
155C22×C4×C11—42no—
156C22×C4×C11—44no—
157C22×C4×C11—82no—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11#4112yes—
163C22×C4×C11C2411yescharacteristic
164C11×SD16—216no—
165C11×SD16—216no—
166C11×SD16—44no—
167C11×SD16—44no—
168C2×C8×C11—28no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11C2×D414yes—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—44no—
181C11×C4⋊C4—44no—
182C11×C4⋊C4—42no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—44no—
185C11×C22⋊C4—42no—
186C11×C22⋊C4—42no—
187C11×C22⋊C4—44no—
188C11×C22⋊C4—82no—
189C11×C22⋊C4SD1614yescomplemented
190C42×C11—22no—
191C42×C11—22no—
192C23×SD16C2×C1111yescharacteristic
193C2×#461C2×C1112yescomplemented
194C2×#450C2×C1111yescharacteristic
195#2434C2×C1111yescharacteristic, complemented
196D4×C22⋊C4C2×C1111yescharacteristic
197#2055C2×C1112yescomplemented
198#2013C2×C1112yescomplemented
199#1892C2×C1111yescharacteristic, complemented
200#1877C2×C1112yescomplemented
201#1850C2×C1111yescharacteristic, complemented
202#1787C2×C1111yescharacteristic, complemented
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—24no—
207C23×C11—22no—
208C23×C11—48no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—42no—
216C23×C11—48no—
217C23×C11—84no—
218C23×C11—88no—
219C23×C11—88no—
220C23×C11#12112yes—
221C23×C11C2×SD1612yes—
222C23×C11#13712yes—
223C23×C11C22×D411yescharacteristic
224Q8×C11—24no—
225Q8×C11—24no—
226Q8×C11—48no—
227Q8×C11—42no—
228Q8×C11—42no—
229Q8×C11—41no—
230Q8×C11—41no—
231Q8×C11—42no—
232D4×C11—22no—
233D4×C11—22no—
234D4×C11—22no—
235D4×C11—24no—
236D4×C11—48no—
237D4×C11—42no—
238D4×C11#12014yes—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—22no—
246C2×C4×C11—24no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—48no—
250C2×C4×C11—42no—
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—42no—
258C2×C4×C11—42no—
259C2×C4×C11—88no—
260C2×C4×C11#12112yes—
261C2×C4×C11C2×SD1614yescomplemented
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—
269C23×Q8C22×C1111yescharacteristic
270C23×D4C22×C1111yescharacteristic
271C22×SD16—24no—
272C22×SD16—28no—
273C22×SD16C22×C1112yes—
274C22×SD16C22×C1111yescharacteristic
275C22×SD16C22×C1112yes—
276C22×SD16C22×C1111yescharacteristic
277C23×C8C22×C1111yescharacteristic
278C2×C4⋊Q8C22×C1112yescomplemented
279C2×C22⋊Q8C22×C1111yescharacteristic
280C2×C4×D4C22×C1112yes—
281C22×C22⋊C4—21no—
282#461—28no—
283#450—24no—
284C2×C4⋊C8C22×C1112yescomplemented
285C2×#103C22×C1112yescomplemented
286C2×#103C22×C1112yescomplemented
287C2×#103C22×C1112yescomplemented
288C2×#102C22×C1111yescharacteristic
289C2×#102C22×C1111yescharacteristic
290C2×C22⋊C8C22×C1111yescharacteristic
291#395—22no—
292#391C22×C1112yescomplemented
293#390C22×C1112yes—
294#386—22no—
295#385—21no—
296#385—21no—
297#380C22×C1111yescharacteristic
298#379—21no—
299C4×C22⋊C4C22×C1111yescharacteristic
300#340C22×C1112yescomplemented
301#336C22×C1112yescomplemented
302C22×C11—22no—
303C22×C11—24no—
304C22×C11—24no—
305C22×C11—22no—
306C22×C11—24no—
307C22×C11—44no—
308C22×C11—44no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—816no—
315C22×C11—82no—
316C22×C11—82no—
317C22×C11#46114yescomplemented
318C22×C11C2×#12111yescharacteristic
319C22×C11D4212yes—
320C22×C11C22×SD1611yescharacteristic
321C22×C11C2×#13711yescharacteristic
322C22×C11#57712yes—
323C4×C11—22no—
324C4×C11—24no—
325C4×C11—44no—
326C4×C11—42no—
327C4×C11—81no—
328C4×C11—82no—
329C4×C11—81no—
330C4×C11C2×#12011yescharacteristic
331C4×C11#53411yescharacteristic
332C4×C11#54612yes—
333C25—21no—
334C22×Q8—21no—
335C22×Q8—24no—
336C22×Q8—22no—
337C22×Q8—22no—
338C22×Q8—42no—
339C22×Q8C23×C1111yescharacteristic
340C22×Q8C23×C1112yes—
341C22×D4—24no—
342C22×D4—21no—
343C22×D4—22no—
344C22×D4—42no—
345C22×D4D4×C1114yes—
346C22×D4C23×C1111yescharacteristic
347C22×D4C23×C1111yescharacteristic
348C23×C4—21no—
349C23×C4—22no—
350C23×C4C23×C1111yescharacteristic
351C2×SD16—232no—
352C2×SD16—24no—
353C2×SD16—24no—
354C2×SD16—24no—
355C2×SD16—24no—
356C2×SD16—22no—
357C2×SD16—22no—
358C2×SD16—24no—
359C2×SD16—24no—
360C2×SD16—42no—
361C2×SD16D4×C1118yes—
362C22×C8—22no—
363C22×C8—24no—
364C22×C8C23×C1111yescharacteristic
365C22×C8C23×C1111yescharacteristic
366C22×C8C23×C1112yes—
367C4⋊Q8—24no—
368C4⋊Q8—42no—
369C22⋊Q8—22no—
370C22⋊Q8—22no—
371C4×D4—24no—
372C4×D4—42no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4C23×C1112yes—
377C2×C4⋊C4C23×C1111yescharacteristic
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4D4×C1111yescharacteristic
385C2×C22⋊C4D4×C1111yescharacteristic
386C2×C42C23×C1112yes—
387C4⋊C8—24no—
388#103—24no—
389#103—24no—
390#103—42no—
391#102—22no—
392#102—22no—
393C22⋊C8—22no—
394#95—21no—
395#95—22no—
396#95—22no—
397#95D4×C1112yes—
398C2×C11—24no—
399C2×C11—44no—
400C2×C11—82no—
401C2×C11#241011yescharacteristic
402C2×C11C2×#46111yescharacteristic
403C2×C11#304211yescharacteristic
404C2×C11#326612yes—
405C2×C11D4×SD1612yes—
406C24—21no—
407C24—21no—
408C24—24no—
409C24—44no—
410C24—42no—
411C24—42no—
412C24—82no—
413C24C2×D4×C1111yescharacteristic
414C2×Q8—22no—
415C2×Q8—28no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—21no—
420C2×Q8—22no—
421C2×Q8—21no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—44no—
425C2×Q8—48no—
426C2×Q8—44no—
427C2×Q8—42no—
428C2×Q8C2×D4×C1114yes—
429C2×D4—28no—
430C2×D4—24no—
431C2×D4—22no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—44no—
437C2×D4—48no—
438C2×D4—44no—
439C2×D4C2×D4×C1112yes—
440C2×D4C2×D4×C1112yes—
441C2×D4C2×D4×C1114yes—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—44no—
449C22×C4—44no—
450C22×C4—42no—
451C22×C4—44no—
452C22×C4—82no—
453C22×C4C2×D4×C1112yes—
454C22×C4C2×D4×C1111yescharacteristic
455C22×C4C2×D4×C1112yes—
456C22×C4C2×D4×C1112yes—
457C22×C4C11×#4112yes—
458C22×C4C24×C1111yescharacteristic
459SD16—216no—
460SD16—216no—
461SD16—44no—
462SD16—44no—
463C2×C8—28no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8C2×D4×C1114yes—
471C4⋊C4—21no—
472C4⋊C4—22no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4—44no—
476C4⋊C4—44no—
477C4⋊C4—42no—
478C22⋊C4—22no—
479C22⋊C4—44no—
480C22⋊C4—42no—
481C22⋊C4—42no—
482C22⋊C4—44no—
483C22⋊C4—82no—
484C22⋊C4C11×SD1614yescomplemented
485C42—22no—
486C42—22no—
487C11#2435811yescharacteristic, direct product factor, Sylow
488C23—22no—
489C23—22no—
490C23—22no—
491C23—24no—
492C23—22no—
493C23—48no—
494C23—41no—
495C23—41no—
496C23—42no—
497C23—42no—
498C23—41no—
499C23—41no—
500C23—42no—
501C23—48no—
502C23—84no—
503C23—88no—
504C23—88no—
505C23C11×#12112yes—
506C23C2×C11×SD1612yes—
507C23C11×#13712yes—
508C23C22×D4×C1111yescharacteristic
509Q8—24no—
510Q8—24no—
511Q8—48no—
512Q8—42no—
513Q8—42no—
514Q8—41no—
515Q8—41no—
516Q8—42no—
517D4—22no—
518D4—22no—
519D4—22no—
520D4—24no—
521D4—48no—
522D4—42no—
523D4C11×#12014yes—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—48no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—88no—
545C2×C4C11×#12112yes—
546C2×C4C2×C11×SD1614yescomplemented
547C2×C4C22×D4×C1111yescharacteristic
548C2×C4C22×D4×C1112yes—
549C2×C4C2×C11×#4111yescharacteristic
550C2×C4C11×H(5,𝔽2)12yes—
551C8—24no—
552C8—41no—
553C8—41no—
554C22—22no—
555C22—24no—
556C22—24no—
557C22—22no—
558C22—24no—
559C22—44no—
560C22—44no—
561C22—42no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—42no—
566C22—816no—
567C22—82no—
568C22—82no—
569C22C11×#46114yescomplemented
570C22C2×C11×#12111yescharacteristic
571C22D42×C1112yes—
572C22C22×C11×SD1611yescharacteristic
573C22C2×C11×#13711yescharacteristic
574C22C11×#57712yes—
575C4—22no—
576C4—24no—
577C4—44no—
578C4—42no—
579C4—81no—
580C4—82no—
581C4—81no—
582C4C2×C11×#12011yescharacteristic
583C4C11×#53411yescharacteristic
584C4C11×#54612yes—
585C2—24no—
586C2—44no—
587C2—82no—
588C2C11×#241011yescharacteristic
589C2C2×C11×#46111yescharacteristic
590C2C11×#304211yescharacteristic
591C2C11×#326612yes—
592C2D4×C11×SD1612yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC23×D4×C11C22
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×#461C2semidirect
4. C11×#2434C2semidirect
6. C11×#2055C2semidirect
7. C11×#2013C2semidirect
8. C11×#1892C2semidirect
9. C11×#1877C2semidirect
10. C11×#1850C2semidirect
11. C11×#1787C2semidirect
21. C2×C11×C4⋊Q8C22semidirect
27. C2×C11×C4⋊C8C22semidirect
28. C2×C11×#103C22semidirect
29. C2×C11×#103C22semidirect
30. C2×C11×#103C22semidirect
35. C11×#391C22semidirect
43. C11×#340C22semidirect
44. C11×#336C22semidirect
110. #24358C11direct (N × H)
189. C11×C22⋊C4SD16semidirect
193. C2×#461C2×C11semidirect
195. #2434C2×C11semidirect
197. #2055C2×C11semidirect
198. #2013C2×C11semidirect
199. #1892C2×C11semidirect
200. #1877C2×C11semidirect
201. #1850C2×C11semidirect
202. #1787C2×C11semidirect
261. C2×C4×C11C2×SD16semidirect
278. C2×C4⋊Q8C22×C11semidirect
284. C2×C4⋊C8C22×C11semidirect
285. C2×#103C22×C11semidirect
286. C2×#103C22×C11semidirect
287. C2×#103C22×C11semidirect
292. #391C22×C11semidirect
300. #340C22×C11semidirect
301. #336C22×C11semidirect
317. C22×C11#461semidirect
484. C22⋊C4C11×SD16semidirect
487. C11#24358direct (N × H)
546. C2×C4C2×C11×SD16semidirect
569. C22C11×#461semidirect

Maximal subgroups

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

subgroupindex
C23×C11×SD162
C2×C11×#4612
C2×C11×#4502
C11×#24342
D4×C11×C22⋊C42
C11×#20552
C11×#20132
C11×#18922
C11×#18772
C11×#18502
C11×#17872
#2435811