Finite Group Databasebeta

← C11×#24089 #14601282

Subgroups — C11×#24089 #14601282

Order 2816.

1334 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#547C211yesmaximal, characteristic
2C2×C11×#481C211yesmaximal, characteristic, complemented
3C22×C11×#106C211yesmaximal, characteristic, complemented
4C11×#2487C211yesmaximal, characteristic, complemented
5C11×#2058C212yesmaximal, complemented
6C11×#2034C212yesmaximal, complemented
7C11×#1893C211yesmaximal, characteristic, complemented
8C11×#1869C211yesmaximal, characteristic, complemented
9C11×#1864C212yesmaximal, complemented
10C11×#1853C212yesmaximal, complemented
11C11×#1823C211yesmaximal, characteristic, complemented
12C22×C11×#41—21no—
13C23×C8×C11C2211yescharacteristic
14C11×#547—24no—
15C11×#547—24no—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#123—21no—
18C2×C11×#123—21no—
19C2×C11×C22⋊Q8—21no—
20C2×C11×#121C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C11×#481—24no—
28C2×C11×#106—24no—
29C2×C11×#106C2212yes—
30C2×C11×#106C2212yes—
31C2×C11×#106C2212yes—
32C2×C11×#102C2212yes—
33C2×C11×#102C2212yes—
34C2×C11×C22⋊C8C2212yes—
35C2×C11×C22⋊C8C2211yescharacteristic
36C11×#400—21no—
37C11×#399—21no—
38C11×#389C2212yes—
39C11×#386—21no—
40C11×#385—21no—
41C11×#380C2211yescharacteristic
42C11×#380C2212yes—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C11×#340C2212yes—
46C11×#336C2212yes—
47C2×C11×#41—28no—
48C2×C11×#41—44no—
49C2×C11×#41—44no—
50C22×Q8×C11—21no—
51C22×D4×C11—21no—
52C22×D4×C11—21no—
53C22×D4×C11D411yescharacteristic
54C22×D4×C11C2311yescharacteristic
55C23×C4×C11—21no—
56C23×C4×C11—21no—
57C23×C4×C11—21no—
58C23×C4×C11—21no—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C22×C8×C11—22no—
62C22×C8×C11—24no—
63C22×C8×C11C2312yes—
64C22×C8×C11C2312yes—
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8—22no—
67C11×#123—28no—
68C11×#123—28no—
69C11×C22⋊Q8—28no—
70C11×#121—22no—
71C11×#121—22no—
72C11×#121—22no—
73C11×#121D414yes—
74C4×D4×C11—22no—
75C4×D4×C11—22no—
76C4×D4×C11—22no—
77C4×D4×C11—22no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4D411yescharacteristic
89C2×C11×C4⋊C4D414yes—
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—22no—
100C2×C11×C22⋊C4D411yescharacteristic
101C2×C11×C22⋊C4D411yescharacteristic
102C2×C42×C11C2311yescharacteristic
103C11×#106—24no—
104C11×#106—24no—
105C11×#106—24no—
106C11×#102—24no—
107C11×#102—24no—
108C11×C22⋊C8—22no—
109C11×C22⋊C8—24no—
110C11×#95—22no—
111C11×#95—21no—
112C11×#95—22no—
113#24089C1111yesmaximal, characteristic, direct product factor, Sylow
114C24×C11—21no—
115C24×C11C2×D411yescharacteristic
116C24×C11C2×D411yescharacteristic
117C11×#41—432no—
118C2×Q8×C11—24no—
119C2×Q8×C11—42no—
120C2×Q8×C11—42no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—24no—
124C2×D4×C11—24no—
125C2×D4×C11—21no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—42no—
129C2×D4×C11—42no—
130C2×D4×C11—42no—
131C2×D4×C11—42no—
132C2×D4×C11SD1614yes—
133C2×D4×C11C2×D412yes—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11—42no—
154C22×C4×C11—42no—
155C22×C4×C11—82no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2411yescharacteristic
163C2×C8×C11—28no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11#4114yescomplemented
170C11×C4⋊C4—24no—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—42no—
182C11×C4⋊C4—82no—
183C11×C4⋊C4C2×D412yes—
184C11×C4⋊C4C2×D412yes—
185C11×C4⋊C4C2×D412yes—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—24no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—24no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—42no—
192C11×C22⋊C4—82no—
193C42×C11—21no—
194C42×C11—21no—
195C2×#547C2×C1111yescharacteristic
196C2×#481C2×C1111yescharacteristic, complemented
197C22×#106C2×C1111yescharacteristic, complemented
198#2487C2×C1111yescharacteristic, complemented
199#2058C2×C1112yescomplemented
200#2034C2×C1112yescomplemented
201#1893C2×C1111yescharacteristic, complemented
202#1869C2×C1111yescharacteristic, complemented
203#1864C2×C1112yescomplemented
204#1853C2×C1112yescomplemented
205#1823C2×C1111yescharacteristic, complemented
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—21no—
209C23×C11—22no—
210C23×C11—21no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—42no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—42no—
217C23×C11#12012yes—
218C23×C11C2×SD1612yes—
219C23×C11C2×SD1612yes—
220C23×C11AGL(1,ℤ/8)12yes—
221C23×C11C22×D411yescharacteristic
222Q8×C11—48no—
223D4×C11—28no—
224D4×C11—24no—
225D4×C11—48no—
226D4×C11—48no—
227D4×C11—41no—
228D4×C11—41no—
229C2×C4×C11—21no—
230C2×C4×C11—22no—
231C2×C4×C11—21no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—48no—
243C2×C4×C11—48no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—48no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—84no—
261C2×C4×C11#12012yes—
262C2×C4×C11C2×SD1612yes—
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C2×#4112yes—
266C2×C4×C112−1+412yes—
267C8×C11—24no—
268C8×C11—42no—
269C22×#41—21no—
270C23×C8C22×C1111yescharacteristic
271#547—24no—
272#547—24no—
273C2×C4⋊Q8C22×C1111yescharacteristic
274C2×#123—21no—
275C2×#123—21no—
276C2×C22⋊Q8—21no—
277C2×#121C22×C1111yescharacteristic
278C2×#121C22×C1111yescharacteristic
279C2×C4×D4C22×C1111yescharacteristic
280C2×C4×D4C22×C1111yescharacteristic
281C22×C4⋊C4C22×C1111yescharacteristic
282C22×C4⋊C4C22×C1111yescharacteristic
283C22×C4⋊C4C22×C1111yescharacteristic
284#481—24no—
285C2×#106—24no—
286C2×#106C22×C1112yes—
287C2×#106C22×C1112yes—
288C2×#106C22×C1112yes—
289C2×#102C22×C1112yes—
290C2×#102C22×C1112yes—
291C2×C22⋊C8C22×C1111yescharacteristic
292C2×C22⋊C8C22×C1112yes—
293#400—21no—
294#399—21no—
295#389C22×C1112yes—
296#386—21no—
297#385—21no—
298#380C22×C1111yescharacteristic
299#380C22×C1112yes—
300#340C22×C1112yes—
301#340C22×C1112yes—
302#340C22×C1112yes—
303#336C22×C1112yes—
304C22×C11—24no—
305C22×C11—24no—
306C22×C11—22no—
307C22×C11—22no—
308C22×C11—24no—
309C22×C11—22no—
310C22×C11—42no—
311C22×C11—41no—
312C22×C11—41no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—82no—
317C22×C11—82no—
318C22×C11#45014yes—
319C22×C11C2×#12011yescharacteristic
320C22×C11#54712yes—
321C22×C11C22×SD1611yescharacteristic
322C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
323C22×C11#57712yes—
324C4×C11—22no—
325C4×C11—22no—
326C4×C11—41no—
327C4×C11—42no—
328C4×C11—42no—
329C4×C11—42no—
330C4×C11—41no—
331C4×C11—82no—
332C4×C11—82no—
333C4×C11#52511yescharacteristic
334C4×C11#53611yescharacteristic
335C4×C11#54712yes—
336C2×#41—28no—
337C2×#41—44no—
338C2×#41—44no—
339C22×Q8—21no—
340C22×D4—21no—
341C22×D4—21no—
342C22×D4D4×C1111yescharacteristic
343C22×D4C23×C1111yescharacteristic
344C23×C4—21no—
345C23×C4—21no—
346C23×C4—21no—
347C23×C4—21no—
348C23×C4C23×C1111yescharacteristic
349C23×C4C23×C1111yescharacteristic
350C22×C8—22no—
351C22×C8—24no—
352C22×C8C23×C1112yes—
353C22×C8C23×C1112yes—
354C4⋊Q8—22no—
355C4⋊Q8—22no—
356#123—28no—
357#123—28no—
358C22⋊Q8—28no—
359#121—22no—
360#121—22no—
361#121—22no—
362#121D4×C1114yes—
363C4×D4—22no—
364C4×D4—22no—
365C4×D4—22no—
366C4×D4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4D4×C1111yescharacteristic
378C2×C4⋊C4D4×C1114yes—
379C2×C4⋊C4C23×C1112yes—
380C2×C4⋊C4C23×C1112yes—
381C2×C4⋊C4C23×C1111yescharacteristic
382C2×C4⋊C4C23×C1111yescharacteristic
383C2×C4⋊C4C23×C1111yescharacteristic
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4D4×C1111yescharacteristic
390C2×C22⋊C4D4×C1111yescharacteristic
391C2×C42C23×C1111yescharacteristic
392#106—24no—
393#106—24no—
394#106—24no—
395#102—24no—
396#102—24no—
397C22⋊C8—22no—
398C22⋊C8—24no—
399#95—22no—
400#95—21no—
401#95—22no—
402C2×C11—24no—
403C2×C11—42no—
404C2×C11—82no—
405C2×C11#240611yescharacteristic
406C2×C11C2×#45011yescharacteristic
407C2×C11#301011yescharacteristic
408C2×C11#333512yes—
409C2×C11#334512yes—
410C24—21no—
411C24C2×D4×C1111yescharacteristic
412C24C2×D4×C1111yescharacteristic
413#41—432no—
414C2×Q8—24no—
415C2×Q8—42no—
416C2×Q8—42no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—24no—
420C2×D4—24no—
421C2×D4—21no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4—42no—
428C2×D4C11×SD1614yes—
429C2×D4C2×D4×C1112yes—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—82no—
452C22×C4C2×D4×C1111yescharacteristic
453C22×C4C2×D4×C1111yescharacteristic
454C22×C4C2×D4×C1111yescharacteristic
455C22×C4C2×D4×C1112yes—
456C22×C4C2×D4×C1112yes—
457C22×C4C2×D4×C1111yescharacteristic
458C22×C4C24×C1111yescharacteristic
459C2×C8—28no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8C11×#4114yescomplemented
466C4⋊C4—24no—
467C4⋊C4—24no—
468C4⋊C4—24no—
469C4⋊C4—22no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—42no—
478C4⋊C4—82no—
479C4⋊C4C2×D4×C1112yes—
480C4⋊C4C2×D4×C1112yes—
481C4⋊C4C2×D4×C1112yes—
482C22⋊C4—24no—
483C22⋊C4—24no—
484C22⋊C4—22no—
485C22⋊C4—24no—
486C22⋊C4—22no—
487C22⋊C4—42no—
488C22⋊C4—82no—
489C42—21no—
490C42—21no—
491C11#2408911yescharacteristic, direct product factor, Sylow
492C23—22no—
493C23—22no—
494C23—21no—
495C23—22no—
496C23—21no—
497C23—22no—
498C23—22no—
499C23—42no—
500C23—41no—
501C23—41no—
502C23—42no—
503C23C11×#12012yes—
504C23C2×C11×SD1612yes—
505C23C2×C11×SD1612yes—
506C23C11×AGL(1,ℤ/8)12yes—
507C23C22×D4×C1111yescharacteristic
508Q8—48no—
509D4—28no—
510D4—24no—
511D4—48no—
512D4—48no—
513D4—41no—
514D4—41no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—48no—
529C2×C4—48no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—48no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—84no—
547C2×C4C11×#12012yes—
548C2×C4C2×C11×SD1612yes—
549C2×C4C22×D4×C1111yescharacteristic
550C2×C4C22×D4×C1111yescharacteristic
551C2×C4C2×C11×#4112yes—
552C2×C4C11×2−1+412yes—
553C8—24no—
554C8—42no—
555C22—22no—
556C22—22no—
557C22—24no—
558C22—24no—
559C22—22no—
560C22—24no—
561C22—41no—
562C22—41no—
563C22—42no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—82no—
568C22—82no—
569C22C11×#45014yes—
570C22C2×C11×#12011yescharacteristic
571C22C11×#54712yes—
572C22C22×C11×SD1611yescharacteristic
573C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
574C22C11×#57712yes—
575C4—22no—
576C4—22no—
577C4—41no—
578C4—42no—
579C4—42no—
580C4—42no—
581C4—41no—
582C4—82no—
583C4—82no—
584C4C11×#52511yescharacteristic
585C4C11×#53611yescharacteristic
586C4C11×#54712yes—
587C2—24no—
588C2—42no—
589C2—82no—
590C2C11×#240611yescharacteristic
591C2C2×C11×#45011yescharacteristic
592C2C11×#301011yescharacteristic
593C2C11×#333512yes—
594C2C11×#334512yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#547C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#481C2semidirect
3. C22×C11×#106C2semidirect
4. C11×#2487C2semidirect
5. C11×#2058C2semidirect
6. C11×#2034C2semidirect
7. C11×#1893C2semidirect
8. C11×#1869C2semidirect
9. C11×#1864C2semidirect
10. C11×#1853C2semidirect
11. C11×#1823C2semidirect
113. #24089C11direct (N × H)
169. C2×C8×C11#41semidirect
196. C2×#481C2×C11semidirect
197. C22×#106C2×C11semidirect
198. #2487C2×C11semidirect
199. #2058C2×C11semidirect
200. #2034C2×C11semidirect
201. #1893C2×C11semidirect
202. #1869C2×C11semidirect
203. #1864C2×C11semidirect
204. #1853C2×C11semidirect
205. #1823C2×C11semidirect
465. C2×C8C11×#41semidirect
491. C11#24089direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5472
C2×C11×#4812
C22×C11×#1062
C11×#24872
C11×#20582
C11×#20342
C11×#18932
C11×#18692
C11×#18642
C11×#18532
C11×#18232
#2408911