Finite Group Databasebeta

← C11×#24118 #14601311

Subgroups — C11×#24118 #14601311

Order 2816.

1218 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#554C211yesmaximal, characteristic, complemented
2C2×C11×#476C211yesmaximal, characteristic, complemented
3C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
4C11×#2537C211yesmaximal, characteristic
5C11×#2035C212yesmaximal, complemented
6C11×#2000C212yesmaximal, complemented
7C11×#1990C211yesmaximal, characteristic, complemented
8C11×#1954C211yesmaximal, characteristic, complemented
9C11×#1874C212yesmaximal, complemented
10C11×#1853C212yesmaximal, complemented
11C11×#1803C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2211yescharacteristic
13C11×#554—24no—
14C11×#554—24no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#125—21no—
17C2×C11×C22⋊Q8—22no—
18C2×C11×C22⋊Q8C2212yes—
19C2×C11×#121—21no—
20C2×C11×#121C2212yes—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×D4×C11—21no—
23C2×C4×D4×C11C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C22×C11×C4⋊C4C2212yes—
26C11×#476—24no—
27C4×C11×SD16—24no—
28C2×C11×#106C2211yescharacteristic
29C2×C11×#106C2212yes—
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2212yes—
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2212yes—
35C2×C11×C22⋊C8C2212yes—
36C2×C11×C22⋊C8C2212yes—
37C2×C4×C8×C11C2211yescharacteristic
38C11×#394—22no—
39C11×#384C2211yescharacteristic
40C11×#380—21no—
41C11×#380C2212yes—
42C11×#340C2212yes—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C22×Q8×C11—21no—
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11—22no—
48C22×D4×C11D411yescharacteristic
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—22no—
51C23×C4×C11—21no—
52C23×C4×C11C2312yes—
53C2×C11×SD16—22no—
54C2×C11×SD16—22no—
55C2×C11×SD16—22no—
56C22×C8×C11C2311yescharacteristic
57C22×C8×C11C2312yes—
58C22×C8×C11C2311yescharacteristic
59C11×C4⋊Q8—22no—
60C11×C4⋊Q8D414yescomplemented
61C11×#125—28no—
62C11×C22⋊Q8—216no—
63C11×C22⋊Q8—24no—
64C11×C22⋊Q8—24no—
65C11×#121—24no—
66C11×#121—42no—
67C11×#121—44no—
68C4×Q8×C11—22no—
69C4×Q8×C11D414yescomplemented
70C4×D4×C11—28no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C4×D4×C11—22no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—24no—
80C2×C11×C4⋊C4—24no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4D412yes—
93C2×C42×C11—21no—
94C2×C42×C11C2311yescharacteristic
95C11×#106—22no—
96C11×#106—24no—
97C11×C4⋊C8—22no—
98C11×#103—22no—
99C11×#103—42no—
100C11×#102—22no—
101C11×#102—24no—
102C11×C22⋊C8—24no—
103C11×C22⋊C8—42no—
104C4×C8×C11—22no—
105C11×#95—22no—
106#24118C1111yesmaximal, characteristic, direct product factor, Sylow
107C24×C11—21no—
108C24×C11C2×D412yes—
109C2×Q8×C11—24no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—81no—
116C2×Q8×C11—81no—
117C2×Q8×C11C2×D412yes—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—44no—
126C2×D4×C11—44no—
127C2×D4×C11—82no—
128C2×D4×C11SD1614yescomplemented
129C2×D4×C11#4112yes—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11—28no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—42no—
143C22×C4×C11—42no—
144C22×C4×C11—42no—
145C22×C4×C11—82no—
146C22×C4×C11—82no—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C11×SD16—28no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—22no—
155C2×C8×C11—21no—
156C2×C8×C11—22no—
157C2×C8×C11—21no—
158C2×C8×C11—22no—
159C2×C8×C11—21no—
160C2×C8×C11#4112yes—
161C11×C4⋊C4—28no—
162C11×C4⋊C4—28no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—42no—
173C11×C4⋊C4—81no—
174C11×C4⋊C4C2×D412yes—
175C11×C4⋊C4C2×D414yes—
176C11×C22⋊C4—28no—
177C11×C22⋊C4—24no—
178C11×C22⋊C4—44no—
179C11×C22⋊C4—44no—
180C11×C22⋊C4—42no—
181C42×C11—24no—
182C42×C11C2×D412yes—
183C42×C11C2×D412yes—
184C2×#554C2×C1111yescharacteristic, complemented
185C2×#476C2×C1111yescharacteristic, complemented
186C2×C4×SD16C2×C1111yescharacteristic, complemented
187#2537C2×C1111yescharacteristic
188#2035C2×C1112yescomplemented
189#2000C2×C1112yescomplemented
190#1990C2×C1111yescharacteristic, complemented
191#1954C2×C1111yescharacteristic, complemented
192#1874C2×C1112yescomplemented
193#1853C2×C1112yescomplemented
194#1803C2×C1111yescharacteristic, complemented
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11C2×SD1614yes—
209C23×C11C22×D411yescharacteristic
210Q8×C11—22no—
211Q8×C11—22no—
212Q8×C11—41no—
213Q8×C11—41no—
214Q8×C11—84no—
215D4×C11—22no—
216D4×C11—22no—
217D4×C11—28no—
218D4×C11—41no—
219D4×C11—41no—
220D4×C11—88no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—42no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—41no—
240C2×C4×C11—42no—
241C2×C4×C11—41no—
242C2×C4×C11—42no—
243C2×C4×C11—41no—
244C2×C4×C11—42no—
245C2×C4×C11—88no—
246C2×C4×C11—84no—
247C2×C4×C11#12012yes—
248C2×C4×C11#12012yes—
249C2×C4×C11C2×SD1612yes—
250C2×C4×C11#13712yes—
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11H(5,𝔽2)11yescharacteristic
256C2×C4×C112−1+411yescharacteristic
257C8×C11—22no—
258C8×C11—41no—
259C8×C11—42no—
260C22×SD16C22×C1111yescharacteristic
261#554—24no—
262#554—24no—
263C2×C4⋊Q8C22×C1111yescharacteristic
264C2×#125—21no—
265C2×C22⋊Q8—22no—
266C2×C22⋊Q8C22×C1112yes—
267C2×#121—21no—
268C2×#121C22×C1112yes—
269C2×C4×Q8C22×C1111yescharacteristic
270C2×C4×D4—21no—
271C2×C4×D4C22×C1111yescharacteristic
272C2×C4×D4C22×C1111yescharacteristic
273C22×C4⋊C4C22×C1112yes—
274#476—24no—
275C4×SD16—24no—
276C2×#106C22×C1111yescharacteristic
277C2×#106C22×C1112yes—
278C2×C4⋊C8C22×C1111yescharacteristic
279C2×#103C22×C1111yescharacteristic
280C2×#103C22×C1112yes—
281C2×#102C22×C1111yescharacteristic
282C2×#102C22×C1112yes—
283C2×C22⋊C8C22×C1112yes—
284C2×C22⋊C8C22×C1112yes—
285C2×C4×C8C22×C1111yescharacteristic
286#394—22no—
287#384C22×C1111yescharacteristic
288#380—21no—
289#380C22×C1112yes—
290#340C22×C1112yes—
291#340C22×C1112yes—
292#340C22×C1112yes—
293C22×C11—24no—
294C22×C11—24no—
295C22×C11—24no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—81no—
304C22×C11—81no—
305C22×C11—81no—
306C22×C11—81no—
307C22×C11C2×#12011yescharacteristic
308C22×C11#54611yescharacteristic
309C22×C11#54711yescharacteristic
310C22×C11C22×SD1611yescharacteristic
311C22×C11C2×#13711yescharacteristic
312C22×C11#57611yescharacteristic
313C22×C11#57711yescharacteristic
314C4×C11—22no—
315C4×C11—42no—
316C4×C11—42no—
317C4×C11—42no—
318C4×C11—44no—
319C4×C11—81no—
320C4×C11—82no—
321C4×C11#44814yes—
322C4×C11#52511yescharacteristic
323C4×C11#53711yescharacteristic
324C4×C11#54811yescharacteristic
325C4×C11#55011yescharacteristic
326C22×Q8—21no—
327C22×Q8C23×C1111yescharacteristic
328C22×D4—22no—
329C22×D4D4×C1111yescharacteristic
330C22×D4C23×C1111yescharacteristic
331C23×C4—22no—
332C23×C4—21no—
333C23×C4C23×C1112yes—
334C2×SD16—22no—
335C2×SD16—22no—
336C2×SD16—22no—
337C22×C8C23×C1111yescharacteristic
338C22×C8C23×C1112yes—
339C22×C8C23×C1111yescharacteristic
340C4⋊Q8—22no—
341C4⋊Q8D4×C1114yescomplemented
342#125—28no—
343C22⋊Q8—216no—
344C22⋊Q8—24no—
345C22⋊Q8—24no—
346#121—24no—
347#121—42no—
348#121—44no—
349C4×Q8—22no—
350C4×Q8D4×C1114yescomplemented
351C4×D4—28no—
352C4×D4—22no—
353C4×D4—22no—
354C4×D4—22no—
355C4×D4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4D4×C1111yescharacteristic
365C2×C4⋊C4C23×C1111yescharacteristic
366C2×C4⋊C4C23×C1112yes—
367C2×C4⋊C4C23×C1111yescharacteristic
368C2×C4⋊C4C23×C1112yes—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4D4×C1112yes—
374C2×C42—21no—
375C2×C42C23×C1111yescharacteristic
376#106—22no—
377#106—24no—
378C4⋊C8—22no—
379#103—22no—
380#103—42no—
381#102—22no—
382#102—24no—
383C22⋊C8—24no—
384C22⋊C8—42no—
385C4×C8—22no—
386#95—22no—
387C2×C11—44no—
388C2×C11—82no—
389C2×C11#240711yescharacteristic
390C2×C11C2×#44811yescharacteristic
391C2×C11#301211yescharacteristic
392C2×C11#329511yescharacteristic
393C2×C11#333111yescharacteristic
394C2×C11#333511yescharacteristic
395C2×C11#335711yescharacteristic
396C24—21no—
397C24C2×D4×C1112yes—
398C2×Q8—24no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—81no—
405C2×Q8—81no—
406C2×Q8C2×D4×C1112yes—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—44no—
415C2×D4—44no—
416C2×D4—82no—
417C2×D4C11×SD1614yescomplemented
418C2×D4C11×#4112yes—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—28no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—82no—
435C22×C4—82no—
436C22×C4C2×D4×C1112yes—
437C22×C4C2×D4×C1111yescharacteristic
438C22×C4C2×D4×C1111yescharacteristic
439C22×C4C24×C1111yescharacteristic
440SD16—28no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—22no—
445C2×C8—22no—
446C2×C8—21no—
447C2×C8—22no—
448C2×C8—21no—
449C2×C8C11×#4112yes—
450C4⋊C4—28no—
451C4⋊C4—28no—
452C4⋊C4—24no—
453C4⋊C4—24no—
454C4⋊C4—22no—
455C4⋊C4—21no—
456C4⋊C4—22no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—42no—
462C4⋊C4—81no—
463C4⋊C4C2×D4×C1112yes—
464C4⋊C4C2×D4×C1114yes—
465C22⋊C4—28no—
466C22⋊C4—24no—
467C22⋊C4—44no—
468C22⋊C4—44no—
469C22⋊C4—42no—
470C42—24no—
471C42C2×D4×C1112yes—
472C42C2×D4×C1112yes—
473C11#2411811yescharacteristic, direct product factor, Sylow
474C23—22no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23C2×C11×SD1614yes—
488C23C22×D4×C1111yescharacteristic
489Q8—22no—
490Q8—22no—
491Q8—41no—
492Q8—41no—
493Q8—84no—
494D4—22no—
495D4—22no—
496D4—28no—
497D4—41no—
498D4—41no—
499D4—88no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—88no—
525C2×C4—84no—
526C2×C4C11×#12012yes—
527C2×C4C11×#12012yes—
528C2×C4C2×C11×SD1612yes—
529C2×C4C11×#13712yes—
530C2×C4C22×D4×C1111yescharacteristic
531C2×C4C22×D4×C1111yescharacteristic
532C2×C4C2×C11×#4111yescharacteristic
533C2×C4C2×C11×#4111yescharacteristic
534C2×C4C11×H(5,𝔽2)11yescharacteristic
535C2×C4C11×2−1+411yescharacteristic
536C8—22no—
537C8—41no—
538C8—42no—
539C22—24no—
540C22—24no—
541C22—24no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22C2×C11×#12011yescharacteristic
554C22C11×#54611yescharacteristic
555C22C11×#54711yescharacteristic
556C22C22×C11×SD1611yescharacteristic
557C22C2×C11×#13711yescharacteristic
558C22C11×#57611yescharacteristic
559C22C11×#57711yescharacteristic
560C4—22no—
561C4—42no—
562C4—42no—
563C4—42no—
564C4—44no—
565C4—81no—
566C4—82no—
567C4C11×#44814yes—
568C4C11×#52511yescharacteristic
569C4C11×#53711yescharacteristic
570C4C11×#54811yescharacteristic
571C4C11×#55011yescharacteristic
572C2—44no—
573C2—82no—
574C2C11×#240711yescharacteristic
575C2C2×C11×#44811yescharacteristic
576C2C11×#301211yescharacteristic
577C2C11×#329511yescharacteristic
578C2C11×#333111yescharacteristic
579C2C11×#333511yescharacteristic
580C2C11×#335711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2537C2
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
1. C2×C11×#554C2semidirect
2. C2×C11×#476C2semidirect
3. C2×C4×C11×SD16C2semidirect
5. C11×#2035C2semidirect
6. C11×#2000C2semidirect
7. C11×#1990C2semidirect
8. C11×#1954C2semidirect
9. C11×#1874C2semidirect
10. C11×#1853C2semidirect
11. C11×#1803C2semidirect
60. C11×C4⋊Q8D4semidirect
69. C4×Q8×C11D4semidirect
106. #24118C11direct (N × H)
128. C2×D4×C11SD16semidirect
184. C2×#554C2×C11semidirect
185. C2×#476C2×C11semidirect
186. C2×C4×SD16C2×C11semidirect
188. #2035C2×C11semidirect
189. #2000C2×C11semidirect
190. #1990C2×C11semidirect
191. #1954C2×C11semidirect
192. #1874C2×C11semidirect
193. #1853C2×C11semidirect
194. #1803C2×C11semidirect
341. C4⋊Q8D4×C11semidirect
350. C4×Q8D4×C11semidirect
417. C2×D4C11×SD16semidirect
473. C11#24118direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5542
C2×C11×#4762
C2×C4×C11×SD162
C11×#25372
C11×#20352
C11×#20002
C11×#19902
C11×#19542
C11×#18742
C11×#18532
C11×#18032
#2411811