Finite Group Databasebeta

← C11×#23923 #14601116

Subgroups — C11×#23923 #14601116

Order 2816.

1948 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#525C212yesmaximal, complemented
2C2×C11×#452C212yesmaximal, complemented
3C2×C11×#449C212yesmaximal, complemented
4C11×#2001C211yesmaximal, characteristic, complemented
5C11×#2000C212yesmaximal, complemented
6C11×#1999C211yesmaximal, characteristic, complemented
7C11×#1875C212yesmaximal, complemented
8C11×#1873C212yesmaximal, complemented
9C11×#1779C211yesmaximal, characteristic, complemented
10C22×C11×#41C2212yes—
11C24×C4×C11C2211yescharacteristic
12C22×C11×Q16C2211yescharacteristic, complemented
13C22×C11×SD16C2212yescomplemented
14C22×C11×D8C2211yescharacteristic, complemented
15C11×#525—28no—
16C11×#525—28no—
17C2×C11×#123—22no—
18C2×C11×C22⋊Q8C2212yes—
19C2×C11×C22⋊Q8C2212yes—
20C2×C11×#121C2212yes—
21C2×C11×#121C2212yes—
22C2×C11×#120—22no—
23C2×C4×D4×C11—22no—
24C2×C4×D4×C11—22no—
25C2×C11×#117C2212yes—
26C11×#452—28no—
27C11×#449—28no—
28C2×C11×#103C2212yescomplemented
29C2×C11×#103C2212yescomplemented
30C2×C11×#102C2212yescomplemented
31C2×C11×#102C2212yescomplemented
32C2×C11×C22⋊C8C2212yes—
33C2×C11×C22⋊C8C2212yes—
34C2×C11×C22⋊C8C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C11×#340C2211yescharacteristic, complemented
37C11×#340C2212yescomplemented
38C11×#340C2211yescharacteristic, complemented
39C25×C11D411yescharacteristic
40C2×C11×#41—24no—
41C2×C11×#41—24no—
42C2×C11×#41—24no—
43C2×C11×#41—24no—
44C2×C11×#41—42no—
45C2×C11×#41—42no—
46C22×Q8×C11C2312yes—
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11—22no—
50C22×D4×C11C2312yes—
51C23×C4×C11—22no—
52C23×C4×C11—24no—
53C23×C4×C11—24no—
54C23×C4×C11—41no—
55C23×C4×C11—41no—
56C23×C4×C11D411yescharacteristic
57C23×C4×C11D412yes—
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2312yes—
60C2×C11×Q16—24no—
61C2×C11×Q16—41no—
62C2×C11×SD16—24no—
63C2×C11×SD16—24no—
64C2×C11×SD16—42no—
65C2×C11×D8—24no—
66C2×C11×D8—41no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2312yes—
69C22×C8×C11C2311yescharacteristic
70C11×#123—216no—
71C11×C22⋊Q8—24no—
72C11×C22⋊Q8—24no—
73C11×C22⋊Q8—24no—
74C11×C22⋊Q8D418yescomplemented
75C11×#121—24no—
76C11×#121—24no—
77C11×#121—24no—
78C11×#121D418yescomplemented
79C11×#120—216no—
80C4×D4×C11—216no—
81C4×D4×C11—216no—
82C11×#117—24no—
83C11×#117—24no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—22no—
93C2×C42×C11—22no—
94C11×#103—24no—
95C11×#103—24no—
96C11×#102—24no—
97C11×#102—24no—
98C11×C22⋊C8—24no—
99C11×C22⋊C8—24no—
100C11×C22⋊C8—41no—
101C11×C22⋊C8—41no—
102#23923C1111yesmaximal, characteristic, direct product factor, Sylow
103C24×C11—24no—
104C24×C11—22no—
105C24×C11—22no—
106C24×C11—41no—
107C24×C11—42no—
108C24×C11—41no—
109C24×C11C2×D412yes—
110C24×C11C2×D411yescharacteristic
111C11×#41—48no—
112C11×#41—48no—
113C11×#41—48no—
114C11×#41—48no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11C2×D414yes—
121C2×D4×C11—28no—
122C2×D4×C11—28no—
123C2×D4×C11—28no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—44no—
130C2×D4×C11—44no—
131C2×D4×C11—44no—
132C2×D4×C11—44no—
133C2×D4×C11—44no—
134C2×D4×C11—44no—
135C2×D4×C11C2×D414yes—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—28no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—41no—
152C22×C4×C11—42no—
153C22×C4×C11—44no—
154C22×C4×C11—48no—
155C22×C4×C11—44no—
156C22×C4×C11—44no—
157C22×C4×C11—44no—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D414yes—
161C22×C4×C11C2×D414yes—
162C22×C4×C11C2411yescharacteristic
163C11×Q16—44no—
164C11×SD16—48no—
165C11×D8—44no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—21no—
171C2×C8×C11—22no—
172C2×C8×C11—21no—
173C11×C4⋊C4—28no—
174C11×C4⋊C4—28no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4C2×D414yes—
178C11×C4⋊C4C2×D414yes—
179C11×C22⋊C4—28no—
180C11×C22⋊C4—28no—
181C11×C22⋊C4—28no—
182C11×C22⋊C4—28no—
183C11×C22⋊C4—28no—
184C42×C11—28no—
185C2×#525C2×C1112yescomplemented
186C2×#452C2×C1112yescomplemented
187C2×#449C2×C1112yescomplemented
188#2001C2×C1111yescharacteristic, complemented
189#2000C2×C1112yescomplemented
190#1999C2×C1111yescharacteristic, complemented
191#1875C2×C1112yescomplemented
192#1873C2×C1112yescomplemented
193#1779C2×C1111yescharacteristic, complemented
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—21no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—21no—
203C23×C11—22no—
204C23×C11—24no—
205C23×C11—44no—
206C23×C11—48no—
207C23×C11—44no—
208C23×C11—48no—
209C23×C11—44no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11#12014yes—
217C23×C11#13512yes—
218C23×C11C22×D411yescharacteristic
219Q8×C11—24no—
220Q8×C11—24no—
221Q8×C11—42no—
222Q8×C11—42no—
223D4×C11—24no—
224D4×C11—24no—
225D4×C11—416no—
226D4×C11—416no—
227D4×C11—416no—
228D4×C11—42no—
229D4×C11—42no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—22no—
239C2×C4×C11—24no—
240C2×C4×C11—21no—
241C2×C4×C11—44no—
242C2×C4×C11—48no—
243C2×C4×C11—416no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—41no—
251C2×C4×C11—42no—
252C2×C4×C11—41no—
253C2×C4×C11#12014yes—
254C2×C4×C11C22×D412yes—
255C2×C4×C11C22×D412yes—
256C2×C4×C11H(5,𝔽2)11yescharacteristic
257C2×C4×C11H(5,𝔽2)11yescharacteristic
258C8×C11—41no—
259C8×C11—42no—
260C8×C11—41no—
261C22×#41C22×C1112yes—
262C24×C4C22×C1111yescharacteristic
263C22×Q16C22×C1111yescharacteristic, complemented
264C22×SD16C22×C1112yescomplemented
265C22×D8C22×C1111yescharacteristic, complemented
266#525—28no—
267#525—28no—
268C2×#123—22no—
269C2×C22⋊Q8C22×C1112yes—
270C2×C22⋊Q8C22×C1112yes—
271C2×#121C22×C1112yes—
272C2×#121C22×C1112yes—
273C2×#120—22no—
274C2×C4×D4—22no—
275C2×C4×D4—22no—
276C2×#117C22×C1112yes—
277#452—28no—
278#449—28no—
279C2×#103C22×C1112yescomplemented
280C2×#103C22×C1112yescomplemented
281C2×#102C22×C1112yescomplemented
282C2×#102C22×C1112yescomplemented
283C2×C22⋊C8C22×C1112yes—
284C2×C22⋊C8C22×C1112yes—
285C2×C22⋊C8C22×C1111yescharacteristic
286C2×C22⋊C8C22×C1111yescharacteristic
287#340C22×C1111yescharacteristic, complemented
288#340C22×C1112yescomplemented
289#340C22×C1111yescharacteristic, complemented
290C22×C11—24no—
291C22×C11—22no—
292C22×C11—24no—
293C22×C11—24no—
294C22×C11—24no—
295C22×C11—416no—
296C22×C11—41no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—41no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—44no—
304C22×C11—44no—
305C22×C11—44no—
306C22×C11—82no—
307C22×C11—82no—
308C22×C11—82no—
309C22×C11—82no—
310C22×C11C2×#12012yes—
311C22×C11#53411yescharacteristic
312C22×C11C2×#13511yescharacteristic
313C22×C11#57511yescharacteristic
314C22×C11#57512yes—
315C4×C11—24no—
316C4×C11—41no—
317C4×C11—44no—
318C4×C11—44no—
319C4×C11—44no—
320C4×C11D4211yescharacteristic
321C4×C11D4212yes—
322C4×C11D4211yescharacteristic
323C25D4×C1111yescharacteristic
324C2×#41—24no—
325C2×#41—24no—
326C2×#41—24no—
327C2×#41—24no—
328C2×#41—42no—
329C2×#41—42no—
330C22×Q8C23×C1112yes—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4C23×C1112yes—
335C23×C4—22no—
336C23×C4—24no—
337C23×C4—24no—
338C23×C4—41no—
339C23×C4—41no—
340C23×C4D4×C1111yescharacteristic
341C23×C4D4×C1112yes—
342C23×C4C23×C1111yescharacteristic
343C23×C4C23×C1112yes—
344C2×Q16—24no—
345C2×Q16—41no—
346C2×SD16—24no—
347C2×SD16—24no—
348C2×SD16—42no—
349C2×D8—24no—
350C2×D8—41no—
351C22×C8C23×C1111yescharacteristic
352C22×C8C23×C1112yes—
353C22×C8C23×C1111yescharacteristic
354#123—216no—
355C22⋊Q8—24no—
356C22⋊Q8—24no—
357C22⋊Q8—24no—
358C22⋊Q8D4×C1118yescomplemented
359#121—24no—
360#121—24no—
361#121—24no—
362#121D4×C1118yescomplemented
363#120—216no—
364C4×D4—216no—
365C4×D4—216no—
366#117—24no—
367#117—24no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4C23×C1112yes—
371C2×C4⋊C4C23×C1112yes—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C42—22no—
378#103—24no—
379#103—24no—
380#102—24no—
381#102—24no—
382C22⋊C8—24no—
383C22⋊C8—24no—
384C22⋊C8—41no—
385C22⋊C8—41no—
386C2×C11—44no—
387C2×C11—42no—
388C2×C11—84no—
389C2×C11#240311yescharacteristic
390C2×C11#300212yes—
391C2×C11#300512yes—
392C2×C11#319111yescharacteristic
393C2×C11#319711yescharacteristic
394C24—24no—
395C24—22no—
396C24—22no—
397C24—41no—
398C24—42no—
399C24—41no—
400C24C2×D4×C1112yes—
401C24C2×D4×C1111yescharacteristic
402#41—48no—
403#41—48no—
404#41—48no—
405#41—48no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8C2×D4×C1114yes—
412C2×D4—28no—
413C2×D4—28no—
414C2×D4—28no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—44no—
421C2×D4—44no—
422C2×D4—44no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—44no—
426C2×D4C2×D4×C1114yes—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—28no—
432C22×C4—24no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—41no—
443C22×C4—42no—
444C22×C4—44no—
445C22×C4—48no—
446C22×C4—44no—
447C22×C4—44no—
448C22×C4—44no—
449C22×C4C2×D4×C1111yescharacteristic
450C22×C4C2×D4×C1112yes—
451C22×C4C2×D4×C1114yes—
452C22×C4C2×D4×C1114yes—
453C22×C4C24×C1111yescharacteristic
454Q16—44no—
455SD16—48no—
456D8—44no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—21no—
462C2×C8—22no—
463C2×C8—21no—
464C4⋊C4—28no—
465C4⋊C4—28no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4C2×D4×C1114yes—
469C4⋊C4C2×D4×C1114yes—
470C22⋊C4—28no—
471C22⋊C4—28no—
472C22⋊C4—28no—
473C22⋊C4—28no—
474C22⋊C4—28no—
475C42—28no—
476C11#2392311yescharacteristic, direct product factor, Sylow
477C23—22no—
478C23—22no—
479C23—22no—
480C23—21no—
481C23—22no—
482C23—22no—
483C23—22no—
484C23—22no—
485C23—21no—
486C23—22no—
487C23—24no—
488C23—44no—
489C23—48no—
490C23—44no—
491C23—48no—
492C23—44no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23C11×#12014yes—
500C23C11×#13512yes—
501C23C22×D4×C1111yescharacteristic
502Q8—24no—
503Q8—24no—
504Q8—42no—
505Q8—42no—
506D4—24no—
507D4—24no—
508D4—416no—
509D4—416no—
510D4—416no—
511D4—42no—
512D4—42no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—21no—
524C2×C4—44no—
525C2×C4—48no—
526C2×C4—416no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4C11×#12014yes—
537C2×C4C22×D4×C1112yes—
538C2×C4C22×D4×C1112yes—
539C2×C4C11×H(5,𝔽2)11yescharacteristic
540C2×C4C11×H(5,𝔽2)11yescharacteristic
541C8—41no—
542C8—42no—
543C8—41no—
544C22—24no—
545C22—22no—
546C22—24no—
547C22—24no—
548C22—24no—
549C22—416no—
550C22—41no—
551C22—42no—
552C22—42no—
553C22—41no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—44no—
558C22—44no—
559C22—44no—
560C22—82no—
561C22—82no—
562C22—82no—
563C22—82no—
564C22C2×C11×#12012yes—
565C22C11×#53411yescharacteristic
566C22C2×C11×#13511yescharacteristic
567C22C11×#57511yescharacteristic
568C22C11×#57512yes—
569C4—24no—
570C4—41no—
571C4—44no—
572C4—44no—
573C4—44no—
574C4D42×C1111yescharacteristic
575C4D42×C1112yes—
576C4D42×C1111yescharacteristic
577C2—44no—
578C2—42no—
579C2—84no—
580C2C11×#240311yescharacteristic
581C2C11×#300212yes—
582C2C11×#300512yes—
583C2C11×#319111yescharacteristic
584C2C11×#319711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#525C2semidirect
2. C2×C11×#452C2semidirect
3. C2×C11×#449C2semidirect
4. C11×#2001C2semidirect
5. C11×#2000C2semidirect
6. C11×#1999C2semidirect
7. C11×#1875C2semidirect
8. C11×#1873C2semidirect
9. C11×#1779C2semidirect
12. C22×C11×Q16C22semidirect
13. C22×C11×SD16C22semidirect
14. C22×C11×D8C22semidirect
28. C2×C11×#103C22semidirect
29. C2×C11×#103C22semidirect
30. C2×C11×#102C22semidirect
31. C2×C11×#102C22semidirect
36. C11×#340C22semidirect
37. C11×#340C22semidirect
38. C11×#340C22semidirect
74. C11×C22⋊Q8D4semidirect
78. C11×#121D4semidirect
102. #23923C11direct (N × H)
185. C2×#525C2×C11semidirect
186. C2×#452C2×C11semidirect
187. C2×#449C2×C11semidirect
188. #2001C2×C11semidirect
189. #2000C2×C11semidirect
190. #1999C2×C11semidirect
191. #1875C2×C11semidirect
192. #1873C2×C11semidirect
193. #1779C2×C11semidirect
263. C22×Q16C22×C11semidirect
264. C22×SD16C22×C11semidirect
265. C22×D8C22×C11semidirect
279. C2×#103C22×C11semidirect
280. C2×#103C22×C11semidirect
281. C2×#102C22×C11semidirect
282. C2×#102C22×C11semidirect
287. #340C22×C11semidirect
288. #340C22×C11semidirect
289. #340C22×C11semidirect
358. C22⋊Q8D4×C11semidirect
362. #121D4×C11semidirect
476. C11#23923direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5252
C2×C11×#4522
C2×C11×#4492
C11×#20012
C11×#20002
C11×#19992
C11×#18752
C11×#18732
C11×#17792
#2392311