Finite Group Databasebeta

← C11×#23394 #14600587

Subgroups — C11×#23394 #14600587

Order 2816.

2014 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#137C211yesmaximal, characteristic, complemented
2C2×C11×#537C211yesmaximal, characteristic
3C2×C11×#536C211yesmaximal, characteristic, complemented
4C2×C11×#416C211yesmaximal, characteristic, complemented
5C22×C11×#103C211yesmaximal, characteristic, complemented
6C2×C11×#408C211yesmaximal, characteristic, complemented
7C11×#2001C214yesmaximal, complemented
8C11×#2000C214yesmaximal, complemented
9C11×#1736C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C22×C11×#41C2211yescharacteristic
12C23×Q8×C11C2211yescharacteristic
13C2×C11×#137—24no—
14C2×C11×#137—24no—
15C2×C11×#137—24no—
16C22×C11×Q16C2212yes—
17C22×C11×SD16C2212yes—
18C22×C11×M16C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C11×#537—24no—
21C11×#537—24no—
22C11×#536—24no—
23C11×#536—24no—
24C2×C11×C4⋊Q8—21no—
25C2×C11×#124—21no—
26C2×C11×#123—22no—
27C2×C11×C22⋊Q8—21no—
28C2×C11×C22⋊Q8C2214yes—
29C2×C11×C22⋊Q8C2212yes—
30C2×C11×#121—21no—
31C2×C11×#121—22no—
32C2×C11×#121C2212yes—
33C2×C11×#117C2211yescharacteristic
34C22×C11×C4⋊C4C2211yescharacteristic
35C11×#416—24no—
36C2×C11×#103—24no—
37C2×C11×#103C2214yes—
38C2×C11×#103C2212yes—
39C2×C11×#102C2212yes—
40C11×#408—24no—
41C2×C11×C22⋊C8C2214yes—
42C11×#340C2214yes—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41—22no—
51C2×C11×#41—22no—
52C2×C11×#41—22no—
53C2×C11×#41—22no—
54C2×C11×#41D414yes—
55C22×Q8×C11—21no—
56C22×Q8×C11—22no—
57C22×Q8×C11—22no—
58C22×Q8×C11—22no—
59C22×Q8×C11—22no—
60C22×Q8×C11—22no—
61C22×Q8×C11D411yescharacteristic
62C22×Q8×C11D414yescomplemented
63C22×Q8×C11C2312yes—
64C22×Q8×C11C2311yescharacteristic
65C22×D4×C11—21no—
66C22×D4×C11—22no—
67C22×D4×C11D412yes—
68C22×D4×C11D411yescharacteristic
69C22×D4×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11—21no—
72C23×C4×C11—21no—
73C23×C4×C11C2312yes—
74C23×C4×C11C2311yescharacteristic
75C11×#137—232no—
76C2×C11×Q16—24no—
77C2×C11×Q16—24no—
78C2×C11×Q16—24no—
79C2×C11×SD16—24no—
80C2×C11×SD16—24no—
81C2×C11×SD16—24no—
82C2×C11×M16—22no—
83C2×C11×M16—22no—
84C2×C11×M16D414yescomplemented
85C22×C8×C11—22no—
86C22×C8×C11—22no—
87C22×C8×C11—22no—
88C22×C8×C11C2312yes—
89C22×C8×C11C2312yes—
90C11×C4⋊Q8—28no—
91C11×#124—28no—
92C11×#123—216no—
93C11×C22⋊Q8—28no—
94C11×C22⋊Q8—28no—
95C11×C22⋊Q8—24no—
96C11×C22⋊Q8—28no—
97C11×C22⋊Q8—24no—
98C11×#121—216no—
99C11×#121—28no—
100C11×#121—24no—
101C11×#121—24no—
102C11×#117—22no—
103C11×#117D414yescomplemented
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—22no—
106C2×C11×C4⋊C4—22no—
107C2×C11×C4⋊C4—24no—
108C2×C11×C4⋊C4D414yes—
109C2×C11×C4⋊C4C2312yes—
110C2×C11×C4⋊C4C2312yes—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—22no—
113C2×C11×C22⋊C4—24no—
114C2×C11×C22⋊C4—22no—
115C2×C42×C11—21no—
116C11×#103—28no—
117C11×#103—24no—
118C11×#102—24no—
119C11×C22⋊C8—28no—
120#23394C1111yesmaximal, characteristic, direct product factor, Sylow
121C24×C11—21no—
122C24×C11C2×D412yes—
123C24×C11C2×D411yescharacteristic
124C11×#41—28no—
125C11×#41—28no—
126C11×#41—44no—
127C11×#41—44no—
128C11×#41—44no—
129C11×#41—44no—
130C11×#41—44no—
131C11×#41—44no—
132C2×Q8×C11—22no—
133C2×Q8×C11—24no—
134C2×Q8×C11—22no—
135C2×Q8×C11—22no—
136C2×Q8×C11—22no—
137C2×Q8×C11—21no—
138C2×Q8×C11—28no—
139C2×Q8×C11—28no—
140C2×Q8×C11—22no—
141C2×Q8×C11—21no—
142C2×Q8×C11—22no—
143C2×Q8×C11—22no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—22no—
147C2×Q8×C11—21no—
148C2×Q8×C11—42no—
149C2×Q8×C11—42no—
150C2×Q8×C11—44no—
151C2×Q8×C11—44no—
152C2×Q8×C11C2×D414yes—
153C2×Q8×C11C2×D412yes—
154C2×D4×C11—24no—
155C2×D4×C11—24no—
156C2×D4×C11—24no—
157C2×D4×C11—24no—
158C2×D4×C11—28no—
159C2×D4×C11—22no—
160C2×D4×C11—22no—
161C2×D4×C11—22no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—42no—
168C2×D4×C11—42no—
169C2×D4×C11—84no—
170C2×D4×C11C2×D412yes—
171C22×C4×C11—24no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—21no—
175C22×C4×C11—22no—
176C22×C4×C11—24no—
177C22×C4×C11—24no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—42no—
185C22×C4×C11—42no—
186C22×C4×C11—42no—
187C22×C4×C11—42no—
188C22×C4×C11—82no—
189C22×C4×C11C2×D412yes—
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D412yes—
192C22×C4×C11C2×D412yes—
193C22×C4×C11C2×D412yes—
194C22×C4×C11C2×D412yes—
195C22×C4×C11C2×D412yes—
196C22×C4×C11#4112yes—
197C22×C4×C11C2411yescharacteristic
198C11×Q16—216no—
199C11×SD16—216no—
200C11×M16—28no—
201C2×C8×C11—22no—
202C2×C8×C11—22no—
203C2×C8×C11—22no—
204C2×C8×C11—22no—
205C2×C8×C11—22no—
206C2×C8×C11—44no—
207C2×C8×C11C2×D414yes—
208C11×C4⋊C4—28no—
209C11×C4⋊C4—216no—
210C11×C4⋊C4—24no—
211C11×C4⋊C4—22no—
212C11×C4⋊C4—22no—
213C11×C4⋊C4C2×D414yes—
214C11×C4⋊C4C2×D414yes—
215C11×C22⋊C4—28no—
216C11×C22⋊C4—28no—
217C11×C22⋊C4—216no—
218C11×C22⋊C4—24no—
219C42×C11—24no—
220C22×#137C2×C1111yescharacteristic, complemented
221C2×#537C2×C1111yescharacteristic
222C2×#536C2×C1111yescharacteristic, complemented
223C2×#416C2×C1111yescharacteristic, complemented
224C22×#103C2×C1111yescharacteristic, complemented
225C2×#408C2×C1111yescharacteristic, complemented
226#2001C2×C1114yescomplemented
227#2000C2×C1114yescomplemented
228#1736C2×C1111yescharacteristic, complemented
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—22no—
235C23×C11—24no—
236C23×C11—24no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11#12012yes—
242C23×C11#12012yes—
243C23×C11#12112yes—
244C23×C11C22×D411yescharacteristic
245Q8×C11—24no—
246Q8×C11—22no—
247Q8×C11—24no—
248Q8×C11—22no—
249Q8×C11—42no—
250Q8×C11—41no—
251Q8×C11—42no—
252Q8×C11—41no—
253Q8×C11—48no—
254Q8×C11—44no—
255D4×C11—22no—
256D4×C11—22no—
257D4×C11—48no—
258D4×C11—48no—
259D4×C11—41no—
260D4×C11—41no—
261D4×C11—44no—
262D4×C11—88no—
263C2×C4×C11—24no—
264C2×C4×C11—24no—
265C2×C4×C11—22no—
266C2×C4×C11—24no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—41no—
271C2×C4×C11—42no—
272C2×C4×C11—41no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—44no—
276C2×C4×C11—42no—
277C2×C4×C11—48no—
278C2×C4×C11—42no—
279C2×C4×C11—42no—
280C2×C4×C11—42no—
281C2×C4×C11—42no—
282C2×C4×C11—48no—
283C2×C4×C11—84no—
284C2×C4×C11#12014yes—
285C2×C4×C11#12012yes—
286C2×C4×C11#12012yes—
287C2×C4×C11#12114yes—
288C2×C4×C11#12114yes—
289C2×C4×C11#12112yes—
290C2×C4×C11#12714yes—
291C2×C4×C11C22×D411yescharacteristic
292C2×C4×C11C22×D411yescharacteristic
293C2×C4×C11C22×D411yescharacteristic
294C2×C4×C11C22×D411yescharacteristic
295C2×C4×C11C22×D411yescharacteristic
296C2×C4×C11C2×#4111yescharacteristic
297C8×C11—24no—
298C8×C11—42no—
299C22×#41C22×C1111yescharacteristic
300C22×#41C22×C1111yescharacteristic
301C23×Q8C22×C1111yescharacteristic
302C2×#137—24no—
303C2×#137—24no—
304C2×#137—24no—
305C22×Q16C22×C1112yes—
306C22×SD16C22×C1112yes—
307C22×M16C22×C1111yescharacteristic
308C23×C8C22×C1111yescharacteristic
309#537—24no—
310#537—24no—
311#536—24no—
312#536—24no—
313C2×C4⋊Q8—21no—
314C2×#124—21no—
315C2×#123—22no—
316C2×C22⋊Q8—21no—
317C2×C22⋊Q8C22×C1114yes—
318C2×C22⋊Q8C22×C1112yes—
319C2×#121—21no—
320C2×#121—22no—
321C2×#121C22×C1112yes—
322C2×#117C22×C1111yescharacteristic
323C22×C4⋊C4C22×C1111yescharacteristic
324#416—24no—
325C2×#103—24no—
326C2×#103C22×C1114yes—
327C2×#103C22×C1112yes—
328C2×#102C22×C1112yes—
329#408—24no—
330C2×C22⋊C8C22×C1114yes—
331#340C22×C1114yes—
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—24no—
335C22×C11—24no—
336C22×C11—42no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—42no—
340C22×C11—42no—
341C22×C11—42no—
342C22×C11—44no—
343C22×C11—44no—
344C22×C11—82no—
345C22×C11—82no—
346C22×C11#39214yes—
347C22×C11C2×#12011yescharacteristic
348C22×C11C2×#12011yescharacteristic
349C22×C11C2×#12111yescharacteristic
350C22×C11#57712yes—
351C22×C11#57812yes—
352C4×C11—42no—
353C4×C11—42no—
354C4×C11—44no—
355C4×C11—44no—
356C4×C11—44no—
357C4×C11#39214yes—
358C4×C11C2×#12011yescharacteristic
359C4×C11C2×#12111yescharacteristic
360C4×C11C2×#12111yescharacteristic
361C4×C11C2×#12711yescharacteristic
362C2×#41—22no—
363C2×#41—22no—
364C2×#41—22no—
365C2×#41—22no—
366C2×#41—22no—
367C2×#41—22no—
368C2×#41—22no—
369C2×#41—22no—
370C2×#41—22no—
371C2×#41—22no—
372C2×#41—22no—
373C2×#41D4×C1114yes—
374C22×Q8—21no—
375C22×Q8—22no—
376C22×Q8—22no—
377C22×Q8—22no—
378C22×Q8—22no—
379C22×Q8—22no—
380C22×Q8D4×C1111yescharacteristic
381C22×Q8D4×C1114yescomplemented
382C22×Q8C23×C1112yes—
383C22×Q8C23×C1111yescharacteristic
384C22×D4—21no—
385C22×D4—22no—
386C22×D4D4×C1112yes—
387C22×D4D4×C1111yescharacteristic
388C22×D4C23×C1111yescharacteristic
389C23×C4—21no—
390C23×C4—21no—
391C23×C4—21no—
392C23×C4C23×C1112yes—
393C23×C4C23×C1111yescharacteristic
394#137—232no—
395C2×Q16—24no—
396C2×Q16—24no—
397C2×Q16—24no—
398C2×SD16—24no—
399C2×SD16—24no—
400C2×SD16—24no—
401C2×M16—22no—
402C2×M16—22no—
403C2×M16D4×C1114yescomplemented
404C22×C8—22no—
405C22×C8—22no—
406C22×C8—22no—
407C22×C8C23×C1112yes—
408C22×C8C23×C1112yes—
409C4⋊Q8—28no—
410#124—28no—
411#123—216no—
412C22⋊Q8—28no—
413C22⋊Q8—28no—
414C22⋊Q8—24no—
415C22⋊Q8—28no—
416C22⋊Q8—24no—
417#121—216no—
418#121—28no—
419#121—24no—
420#121—24no—
421#117—22no—
422#117D4×C1114yescomplemented
423C2×C4⋊C4—21no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4D4×C1114yes—
428C2×C4⋊C4C23×C1112yes—
429C2×C4⋊C4C23×C1112yes—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—24no—
433C2×C22⋊C4—22no—
434C2×C42—21no—
435#103—28no—
436#103—24no—
437#102—24no—
438C22⋊C8—28no—
439C2×C11—24no—
440C2×C11—82no—
441C2×C11—82no—
442C2×C11C2×#39211yescharacteristic
443C2×C11#300911yescharacteristic
444C2×C11#301111yescharacteristic
445C2×C11#301312yes—
446C2×C11#306312yes—
447C24—21no—
448C24C2×D4×C1112yes—
449C24C2×D4×C1111yescharacteristic
450#41—28no—
451#41—28no—
452#41—44no—
453#41—44no—
454#41—44no—
455#41—44no—
456#41—44no—
457#41—44no—
458C2×Q8—22no—
459C2×Q8—24no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—21no—
464C2×Q8—28no—
465C2×Q8—28no—
466C2×Q8—22no—
467C2×Q8—21no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—22no—
473C2×Q8—21no—
474C2×Q8—42no—
475C2×Q8—42no—
476C2×Q8—44no—
477C2×Q8—44no—
478C2×Q8C2×D4×C1114yes—
479C2×Q8C2×D4×C1112yes—
480C2×D4—24no—
481C2×D4—24no—
482C2×D4—24no—
483C2×D4—24no—
484C2×D4—28no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—84no—
496C2×D4C2×D4×C1112yes—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—82no—
515C22×C4C2×D4×C1112yes—
516C22×C4C2×D4×C1111yescharacteristic
517C22×C4C2×D4×C1112yes—
518C22×C4C2×D4×C1112yes—
519C22×C4C2×D4×C1112yes—
520C22×C4C2×D4×C1112yes—
521C22×C4C2×D4×C1112yes—
522C22×C4C11×#4112yes—
523C22×C4C24×C1111yescharacteristic
524Q16—216no—
525SD16—216no—
526M16—28no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—44no—
533C2×C8C2×D4×C1114yes—
534C4⋊C4—28no—
535C4⋊C4—216no—
536C4⋊C4—24no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4C2×D4×C1114yes—
540C4⋊C4C2×D4×C1114yes—
541C22⋊C4—28no—
542C22⋊C4—28no—
543C22⋊C4—216no—
544C22⋊C4—24no—
545C42—24no—
546C11#2339411yescharacteristic, direct product factor, Sylow
547C23—22no—
548C23—22no—
549C23—22no—
550C23—22no—
551C23—22no—
552C23—22no—
553C23—24no—
554C23—24no—
555C23—41no—
556C23—41no—
557C23—42no—
558C23—42no—
559C23C11×#12012yes—
560C23C11×#12012yes—
561C23C11×#12112yes—
562C23C22×D4×C1111yescharacteristic
563Q8—24no—
564Q8—22no—
565Q8—24no—
566Q8—22no—
567Q8—42no—
568Q8—41no—
569Q8—48no—
570Q8—44no—
571Q8—42no—
572Q8—41no—
573D4—22no—
574D4—22no—
575D4—48no—
576D4—48no—
577D4—41no—
578D4—44no—
579D4—41no—
580D4—88no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—22no—
584C2×C4—24no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—48no—
593C2×C4—42no—
594C2×C4—44no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—48no—
600C2×C4—42no—
601C2×C4—84no—
602C2×C4C11×#12014yes—
603C2×C4C11×#12012yes—
604C2×C4C11×#12012yes—
605C2×C4C11×#12114yes—
606C2×C4C11×#12114yes—
607C2×C4C11×#12112yes—
608C2×C4C11×#12714yes—
609C2×C4C22×D4×C1111yescharacteristic
610C2×C4C22×D4×C1111yescharacteristic
611C2×C4C22×D4×C1111yescharacteristic
612C2×C4C22×D4×C1111yescharacteristic
613C2×C4C22×D4×C1111yescharacteristic
614C2×C4C2×C11×#4111yescharacteristic
615C8—24no—
616C8—42no—
617C22—22no—
618C22—22no—
619C22—24no—
620C22—24no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—42no—
626C22—42no—
627C22—44no—
628C22—44no—
629C22—82no—
630C22—82no—
631C22C11×#39214yes—
632C22C2×C11×#12011yescharacteristic
633C22C2×C11×#12011yescharacteristic
634C22C2×C11×#12111yescharacteristic
635C22C11×#57712yes—
636C22C11×#57812yes—
637C4—42no—
638C4—42no—
639C4—44no—
640C4—44no—
641C4—44no—
642C4C11×#39214yes—
643C4C2×C11×#12011yescharacteristic
644C4C2×C11×#12111yescharacteristic
645C4C2×C11×#12111yescharacteristic
646C4C2×C11×#12711yescharacteristic
647C2—24no—
648C2—82no—
649C2—82no—
650C2C2×C11×#39211yescharacteristic
651C2C11×#300911yescharacteristic
652C2C11×#301111yescharacteristic
653C2C11×#301312yes—
654C2C11×#306312yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#537C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#137C2semidirect
3. C2×C11×#536C2semidirect
4. C2×C11×#416C2semidirect
5. C22×C11×#103C2semidirect
6. C2×C11×#408C2semidirect
7. C11×#2001C2semidirect
8. C11×#2000C2semidirect
9. C11×#1736C2semidirect
62. C22×Q8×C11D4semidirect
84. C2×C11×M16D4semidirect
103. C11×#117D4semidirect
120. #23394C11direct (N × H)
220. C22×#137C2×C11semidirect
222. C2×#536C2×C11semidirect
223. C2×#416C2×C11semidirect
224. C22×#103C2×C11semidirect
225. C2×#408C2×C11semidirect
226. #2001C2×C11semidirect
227. #2000C2×C11semidirect
228. #1736C2×C11semidirect
381. C22×Q8D4×C11semidirect
403. C2×M16D4×C11semidirect
422. #117D4×C11semidirect
546. C11#23394direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1372
C2×C11×#5372
C2×C11×#5362
C2×C11×#4162
C22×C11×#1032
C2×C11×#4082
C11×#20012
C11×#20002
C11×#17362
#2339411