Finite Group Databasebeta

← C11×#20989 #14598182

Subgroups — C11×#20989 #14598182

Order 2816.

1874 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×M16C211yesmaximal, characteristic, complemented
2C2×C11×#525C211yesmaximal, characteristic
3C2×C11×#413C212yesmaximal, complemented
4C2×C11×#407C211yesmaximal, characteristic, complemented
5C11×#1901C214yesmaximal, complemented
6C11×#1900C214yesmaximal, complemented
7C11×#1742C212yesmaximal, complemented
8C22×C11×#41C2211yescharacteristic
9C24×C4×C11C2211yescharacteristic
10C22×C11×M16—22no—
11C22×C11×M16—21no—
12C22×C11×M16—28no—
13C22×C11×M16C2214yes—
14C22×C11×M16C2212yes—
15C22×C11×M16C2212yes—
16C23×C8×C11—21no—
17C11×#525—22no—
18C11×#525—21no—
19C11×#525—21no—
20C11×#525—21no—
21C11×#525—22no—
22C11×#525—21no—
23C2×C11×#123C412yes—
24C2×C11×C22⋊Q8C2212yes—
25C2×C11×#121C2212yes—
26C2×C11×#120C412yes—
27C2×C4×D4×C11C414yes—
28C2×C11×#117C2211yescharacteristic
29C11×#413—28no—
30C2×C11×#101C2214yescomplemented
31C2×C11×#100C2214yescomplemented
32C11×#407—21no—
33C11×#407—21no—
34C11×#407C2214yes—
35C2×C11×C22⋊C8—22no—
36C11×#343C2218yescomplemented
37C25×C11C2×C411yescharacteristic
38C2×C11×#41—21no—
39C2×C11×#41—21no—
40C2×C11×#41—21no—
41C2×C11×#41—21no—
42C2×C11×#41—24no—
43C2×C11×#41—24no—
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11C2×C412yes—
46C22×D4×C11C2×C414yes—
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11—24no—
49C23×C4×C11—24no—
50C23×C4×C11C2×C412yes—
51C23×C4×C11C2×C412yes—
52C23×C4×C11C2×C411yescharacteristic
53C23×C4×C11D412yes—
54C23×C4×C11D411yescharacteristic
55C23×C4×C11D411yescharacteristic
56C23×C4×C11D411yescharacteristic
57C23×C4×C11D412yes—
58C23×C4×C11D411yescharacteristic
59C23×C4×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C2×C11×M16—216no—
62C2×C11×M16—28no—
63C2×C11×M16—24no—
64C2×C11×M16—24no—
65C2×C11×M16—22no—
66C2×C11×M16—216no—
67C2×C11×M16—22no—
68C2×C11×M16—24no—
69C2×C11×M16—24no—
70C2×C11×M16D418yescomplemented
71C2×C11×M16C2314yes—
72C2×C11×M16C2314yes—
73C22×C8×C11—28no—
74C22×C8×C11—24no—
75C22×C8×C11—22no—
76C22×C8×C11—22no—
77C11×#123—24no—
78C11×#123—22no—
79C11×#123—22no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8—22no—
84C11×#121—22no—
85C11×#121—22no—
86C11×#121—22no—
87C11×#121—22no—
88C11×#120—22no—
89C11×#120—24no—
90C11×#120—22no—
91C4×D4×C11—24no—
92C4×D4×C11—24no—
93C4×D4×C11—24no—
94C4×D4×C11—24no—
95C11×#117—21no—
96C11×#117—21no—
97C11×#117—21no—
98C11×#117—21no—
99C2×C11×C4⋊C4C2×C414yes—
100C2×C11×C4⋊C4C2312yes—
101C2×C11×C22⋊C4C2×C412yes—
102C2×C11×C22⋊C4C2×C414yes—
103C2×C11×C22⋊C4C2×C414yes—
104C2×C42×C11C2×C412yes—
105C11×#101—28no—
106C11×#100—28no—
107C11×C22⋊C8—24no—
108C11×C22⋊C8—24no—
109#20989C1111yesmaximal, characteristic, direct product factor, Sylow
110C24×C11—24no—
111C24×C11—44no—
112C24×C11C22⋊C411yescharacteristic
113C24×C11C22⋊C412yes—
114C24×C11C22⋊C411yescharacteristic
115C24×C11C22×C412yes—
116C24×C11C22×C412yes—
117C24×C11C22×C411yescharacteristic
118C11×#41—42no—
119C11×#41—42no—
120C11×#41—44no—
121C11×#41—44no—
122C11×#41—42no—
123C11×#41—42no—
124C2×Q8×C11—22no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—22no—
128C2×D4×C11—24no—
129C2×D4×C11—24no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—28no—
133C2×D4×C11—22no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—22no—
137C2×D4×C11—48no—
138C22×C4×C11—24no—
139C22×C4×C11—28no—
140C22×C4×C11—22no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—28no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—22no—
147C22×C4×C11—24no—
148C22×C4×C11—22no—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—28no—
154C22×C4×C11C22⋊C412yes—
155C22×C4×C11C22⋊C412yes—
156C22×C4×C11C22⋊C412yes—
157C22×C4×C11C22⋊C411yescharacteristic
158C22×C4×C11C22⋊C411yescharacteristic
159C22×C4×C11C22⋊C412yes—
160C22×C4×C11C22⋊C412yes—
161C22×C4×C11C22×C412yes—
162C22×C4×C11C22×C412yes—
163C22×C4×C11C22×C414yes—
164C22×C4×C11C22×C411yescharacteristic
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D412yes—
168C22×C4×C11C2×D412yes—
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D414yes—
174C22×C4×C11#4114yes—
175C22×C4×C11C2411yescharacteristic
176C11×M16—216no—
177C11×M16—28no—
178C11×M16—24no—
179C11×M16—24no—
180C11×M16—24no—
181C11×M16—44no—
182C11×M16C2×D418yes—
183C2×C8×C11—216no—
184C2×C8×C11—28no—
185C2×C8×C11—24no—
186C2×C8×C11—24no—
187C2×C8×C11—44no—
188C11×C4⋊C4—24no—
189C11×C4⋊C4—24no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—24no—
195C11×C22⋊C4—24no—
196C11×C22⋊C4—24no—
197C11×C22⋊C4—24no—
198C42×C11—22no—
199C42×C11—22no—
200C23×M16C2×C1111yescharacteristic, complemented
201C2×#525C2×C1111yescharacteristic
202C2×#413C2×C1112yescomplemented
203C2×#407C2×C1111yescharacteristic, complemented
204#1901C2×C1114yescomplemented
205#1900C2×C1114yescomplemented
206#1742C2×C1112yescomplemented
207C23×C11—22no—
208C23×C11—24no—
209C23×C11—24no—
210C23×C11—24no—
211C23×C11—22no—
212C23×C11—24no—
213C23×C11—24no—
214C23×C11—22no—
215C23×C11—24no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—416no—
221C23×C11—44no—
222C23×C11C2×C22⋊C412yes—
223C23×C11C2×C22⋊C411yescharacteristic
224C23×C11C2×C22⋊C411yescharacteristic
225C23×C11C2×C22⋊C412yes—
226C23×C11C4×D414yes—
227C23×C11C23×C411yescharacteristic
228Q8×C11—41no—
229Q8×C11—42no—
230Q8×C11—41no—
231D4×C11—48no—
232D4×C11—44no—
233D4×C11—44no—
234D4×C11—48no—
235D4×C11—41no—
236D4×C11—42no—
237D4×C11—41no—
238C2×C4×C11—24no—
239C2×C4×C11—22no—
240C2×C4×C11—24no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—22no—
254C2×C4×C11—24no—
255C2×C4×C11—44no—
256C2×C4×C11—44no—
257C2×C4×C11—44no—
258C2×C4×C11C2×C22⋊C412yes—
259C2×C4×C11C2×C22⋊C412yes—
260C2×C4×C11C2×C22⋊C411yescharacteristic
261C2×C4×C11C2×C22⋊C411yescharacteristic
262C2×C4×C11C4×D414yes—
263C2×C4×C11#12012yes—
264C2×C4×C11#12012yes—
265C2×C4×C11#12114yes—
266C2×C4×C11#12114yes—
267C2×C4×C11#12312yes—
268C2×C4×C11#12312yes—
269C2×C4×C11C22×D412yes—
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C2×#4112yes—
273C8×C11—28no—
274C8×C11—44no—
275C22×#41C22×C1111yescharacteristic
276C24×C4C22×C1111yescharacteristic
277C22×M16—22no—
278C22×M16—21no—
279C22×M16—28no—
280C22×M16C22×C1112yes—
281C22×M16C22×C1114yes—
282C22×M16C22×C1112yes—
283C23×C8—21no—
284#525—21no—
285#525—21no—
286#525—22no—
287#525—22no—
288#525—21no—
289#525—21no—
290C2×#123C4×C1112yes—
291C2×C22⋊Q8C22×C1112yes—
292C2×#121C22×C1112yes—
293C2×#120C4×C1112yes—
294C2×C4×D4C4×C1114yes—
295C2×#117C22×C1111yescharacteristic
296#413—28no—
297C2×#101C22×C1114yescomplemented
298C2×#100C22×C1114yescomplemented
299#407—21no—
300#407—21no—
301#407C22×C1114yes—
302C2×C22⋊C8—22no—
303#343C22×C1118yescomplemented
304C22×C11—28no—
305C22×C11—22no—
306C22×C11—22no—
307C22×C11—22no—
308C22×C11—22no—
309C22×C11—22no—
310C22×C11—22no—
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—44no—
314C22×C11—48no—
315C22×C11—48no—
316C22×C11—44no—
317C22×C11—44no—
318C22×C11—42no—
319C22×C11—84no—
320C22×C11#38612yes—
321C22×C11#38612yes—
322C22×C11#41314yescomplemented
323C22×C11C22×C22⋊C411yescharacteristic
324C22×C11C2×C4×D412yes—
325C4×C11—22no—
326C4×C11—22no—
327C4×C11—44no—
328C4×C11—42no—
329C4×C11#38612yes—
330C4×C11#38612yes—
331C4×C11C2×#12011yescharacteristic
332C4×C11C2×#12112yes—
333C4×C11C2×#12311yescharacteristic
334C25C2×C4×C1111yescharacteristic
335C2×#41—21no—
336C2×#41—21no—
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—24no—
340C2×#41—24no—
341C22×Q8C23×C1111yescharacteristic
342C22×D4C2×C4×C1112yes—
343C22×D4C2×C4×C1114yes—
344C22×D4C23×C1111yescharacteristic
345C23×C4—24no—
346C23×C4—24no—
347C23×C4C2×C4×C1112yes—
348C23×C4C2×C4×C1112yes—
349C23×C4C2×C4×C1111yescharacteristic
350C23×C4D4×C1111yescharacteristic
351C23×C4D4×C1112yes—
352C23×C4D4×C1111yescharacteristic
353C23×C4D4×C1112yes—
354C23×C4D4×C1111yescharacteristic
355C23×C4D4×C1111yescharacteristic
356C23×C4C23×C1112yes—
357C23×C4C23×C1111yescharacteristic
358C2×M16—216no—
359C2×M16—28no—
360C2×M16—24no—
361C2×M16—24no—
362C2×M16—22no—
363C2×M16—216no—
364C2×M16—22no—
365C2×M16—24no—
366C2×M16—24no—
367C2×M16D4×C1118yescomplemented
368C2×M16C23×C1114yes—
369C2×M16C23×C1114yes—
370C22×C8—28no—
371C22×C8—24no—
372C22×C8—22no—
373C22×C8—22no—
374#123—22no—
375#123—24no—
376#123—22no—
377C22⋊Q8—22no—
378C22⋊Q8—22no—
379C22⋊Q8—22no—
380C22⋊Q8—22no—
381#121—22no—
382#121—22no—
383#121—22no—
384#121—22no—
385#120—22no—
386#120—24no—
387#120—22no—
388C4×D4—24no—
389C4×D4—24no—
390C4×D4—24no—
391C4×D4—24no—
392#117—21no—
393#117—21no—
394#117—21no—
395#117—21no—
396C2×C4⋊C4C2×C4×C1114yes—
397C2×C4⋊C4C23×C1112yes—
398C2×C22⋊C4C2×C4×C1112yes—
399C2×C22⋊C4C2×C4×C1114yes—
400C2×C22⋊C4C2×C4×C1114yes—
401C2×C42C2×C4×C1112yes—
402#101—28no—
403#100—28no—
404C22⋊C8—24no—
405C22⋊C8—24no—
406C2×C11—22no—
407C2×C11—24no—
408C2×C11—22no—
409C2×C11—22no—
410C2×C11—42no—
411C2×C11—82no—
412C2×C11C2×#38611yescharacteristic
413C2×C11C2×#41312yes—
414C24—24no—
415C24—44no—
416C24C11×C22⋊C411yescharacteristic
417C24C11×C22⋊C412yes—
418C24C11×C22⋊C411yescharacteristic
419C24C22×C4×C1112yes—
420C24C22×C4×C1112yes—
421C24C22×C4×C1111yescharacteristic
422#41—42no—
423#41—42no—
424#41—44no—
425#41—44no—
426#41—42no—
427#41—42no—
428C2×Q8—22no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—22no—
432C2×D4—24no—
433C2×D4—24no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—28no—
437C2×D4—22no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—22no—
441C2×D4—48no—
442C22×C4—24no—
443C22×C4—28no—
444C22×C4—22no—
445C22×C4—24no—
446C22×C4—22no—
447C22×C4—28no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—28no—
458C22×C4C11×C22⋊C412yes—
459C22×C4C11×C22⋊C412yes—
460C22×C4C11×C22⋊C412yes—
461C22×C4C11×C22⋊C412yes—
462C22×C4C11×C22⋊C411yescharacteristic
463C22×C4C11×C22⋊C412yes—
464C22×C4C11×C22⋊C411yescharacteristic
465C22×C4C22×C4×C1112yes—
466C22×C4C22×C4×C1112yes—
467C22×C4C22×C4×C1114yes—
468C22×C4C22×C4×C1111yescharacteristic
469C22×C4C2×D4×C1112yes—
470C22×C4C2×D4×C1112yes—
471C22×C4C2×D4×C1112yes—
472C22×C4C2×D4×C1112yes—
473C22×C4C2×D4×C1111yescharacteristic
474C22×C4C2×D4×C1111yescharacteristic
475C22×C4C2×D4×C1111yescharacteristic
476C22×C4C2×D4×C1111yescharacteristic
477C22×C4C2×D4×C1114yes—
478C22×C4C11×#4114yes—
479C22×C4C24×C1111yescharacteristic
480M16—216no—
481M16—28no—
482M16—24no—
483M16—24no—
484M16—24no—
485M16—44no—
486M16C2×D4×C1118yes—
487C2×C8—216no—
488C2×C8—28no—
489C2×C8—24no—
490C2×C8—24no—
491C2×C8—44no—
492C4⋊C4—24no—
493C4⋊C4—24no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—24no—
499C22⋊C4—24no—
500C22⋊C4—24no—
501C22⋊C4—24no—
502C42—22no—
503C42—22no—
504C11#2098911yescharacteristic, direct product factor, Sylow
505C23—22no—
506C23—24no—
507C23—24no—
508C23—24no—
509C23—22no—
510C23—24no—
511C23—24no—
512C23—22no—
513C23—24no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—416no—
519C23—44no—
520C23C2×C11×C22⋊C412yes—
521C23C2×C11×C22⋊C411yescharacteristic
522C23C2×C11×C22⋊C411yescharacteristic
523C23C2×C11×C22⋊C412yes—
524C23C4×D4×C1114yes—
525C23C23×C4×C1111yescharacteristic
526Q8—41no—
527Q8—42no—
528Q8—41no—
529D4—48no—
530D4—44no—
531D4—44no—
532D4—48no—
533D4—41no—
534D4—42no—
535D4—41no—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—44no—
554C2×C4—44no—
555C2×C4—44no—
556C2×C4C2×C11×C22⋊C412yes—
557C2×C4C2×C11×C22⋊C412yes—
558C2×C4C2×C11×C22⋊C411yescharacteristic
559C2×C4C2×C11×C22⋊C411yescharacteristic
560C2×C4C4×D4×C1114yes—
561C2×C4C11×#12012yes—
562C2×C4C11×#12012yes—
563C2×C4C11×#12114yes—
564C2×C4C11×#12114yes—
565C2×C4C11×#12312yes—
566C2×C4C11×#12312yes—
567C2×C4C22×D4×C1112yes—
568C2×C4C22×D4×C1111yescharacteristic
569C2×C4C22×D4×C1111yescharacteristic
570C2×C4C2×C11×#4112yes—
571C8—28no—
572C8—44no—
573C22—28no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—22no—
580C22—22no—
581C22—22no—
582C22—44no—
583C22—48no—
584C22—48no—
585C22—44no—
586C22—42no—
587C22—44no—
588C22—84no—
589C22C11×#38612yes—
590C22C11×#38612yes—
591C22C11×#41314yescomplemented
592C22C22×C11×C22⋊C411yescharacteristic
593C22C2×C4×D4×C1112yes—
594C4—22no—
595C4—22no—
596C4—42no—
597C4—44no—
598C4C11×#38612yes—
599C4C11×#38612yes—
600C4C2×C11×#12011yescharacteristic
601C4C2×C11×#12112yes—
602C4C2×C11×#12311yescharacteristic
603C2—22no—
604C2—24no—
605C2—22no—
606C2—22no—
607C2—42no—
608C2—82no—
609C2C2×C11×#38611yescharacteristic
610C2C2×C11×#41312yes—
subgroupG/H
centerC2×C4×C11C2×C22⋊C4
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC22×C11C22×C22⋊C4
prime radicalC2×C11×#525C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×C11×M16C2semidirect
3. C2×C11×#413C2semidirect
4. C2×C11×#407C2semidirect
5. C11×#1901C2semidirect
6. C11×#1900C2semidirect
7. C11×#1742C2semidirect
30. C2×C11×#101C22semidirect
31. C2×C11×#100C22semidirect
36. C11×#343C22semidirect
70. C2×C11×M16D4semidirect
109. #20989C11direct (N × H)
200. C23×M16C2×C11semidirect
202. C2×#413C2×C11semidirect
203. C2×#407C2×C11semidirect
204. #1901C2×C11semidirect
205. #1900C2×C11semidirect
206. #1742C2×C11semidirect
297. C2×#101C22×C11semidirect
298. C2×#100C22×C11semidirect
303. #343C22×C11semidirect
322. C22×C11#413semidirect
367. C2×M16D4×C11semidirect
504. C11#20989direct (N × H)
591. C22C11×#413semidirect

Maximal subgroups

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

subgroupindex
C23×C11×M162
C2×C11×#5252
C2×C11×#4132
C2×C11×#4072
C11×#19012
C11×#19002
C11×#17422
#2098911