Finite Group Databasebeta

← C11×#32913 #14610106

Subgroups — C11×#32913 #14610106

Order 2816.

1506 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#520C211yesmaximal, characteristic, complemented
2C2×C11×#460C211yesmaximal, characteristic, complemented
3C2×C11×#459C211yesmaximal, characteristic, complemented
4C2×C11×#449C212yesmaximal, complemented
5C11×#2619C211yesmaximal, characteristic, complemented
6C11×#1880C212yesmaximal, complemented
7C11×#1879C212yesmaximal, complemented
8C11×#1874C212yesmaximal, complemented
9C11×#1805C211yesmaximal, characteristic, complemented
10C11×#1804C211yesmaximal, characteristic, complemented
11C11×#1798C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×C11×SD16C2212yes—
14C22×C11×D8C2212yes—
15C2×C11×#127C2211yescharacteristic
16C2×C11×#121C2212yes—
17C11×#520—24no—
18C11×#520—24no—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11—21no—
22C2×C4×D4×C11—21no—
23C2×C4×D4×C11C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C2×C11×#117—21no—
26C2×C11×#117C2211yescharacteristic
27C22×C11×C4⋊C4—21no—
28C22×C11×C4⋊C4C2211yescharacteristic
29C11×#460—24no—
30C11×#459—24no—
31C11×#449—28no—
32C2×C11×C4⋊C8C2211yescharacteristic
33C2×C11×C4⋊C8C2211yescharacteristic
34C2×C11×#103C2212yes—
35C2×C11×#102C2212yes—
36C2×C11×#102C2212yes—
37C2×C11×#102C2212yes—
38C2×C11×C22⋊C8C2212yes—
39C11×#394—21no—
40C11×#394—21no—
41C11×#392—21no—
42C11×#392—21no—
43C11×#390C2212yes—
44C11×#382C2211yescharacteristic
45C11×#340C2212yes—
46C11×#340C2212yes—
47C11×#336C2212yes—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41—22no—
51C2×C11×#41—22no—
52C2×C11×#41—22no—
53C2×C11×#41D414yescomplemented
54C22×Q8×C11C2311yescharacteristic
55C22×D4×C11—21no—
56C22×D4×C11—22no—
57C22×D4×C11—21no—
58C22×D4×C11—21no—
59C22×D4×C11C2312yes—
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11—21no—
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C23×C4×C11C2311yescharacteristic
66C2×C11×SD16—24no—
67C2×C11×SD16—24no—
68C2×C11×SD16—24no—
69C2×C11×D8—24no—
70C2×C11×D8—24no—
71C2×C11×D8—24no—
72C22×C8×C11C2312yes—
73C22×C8×C11C2312yes—
74C11×#127—22no—
75C11×#127—22no—
76C11×#121—24no—
77C11×#121—24no—
78C4×Q8×C11—22no—
79C4×Q8×C11—22no—
80C4×Q8×C11—22no—
81C4×Q8×C11D414yescomplemented
82C4×D4×C11—28no—
83C4×D4×C11—28no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11D414yescomplemented
88C11×#117—28no—
89C11×#117—22no—
90C11×#117—22no—
91C2×C11×C4⋊C4—28no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4D411yescharacteristic
98C2×C11×C4⋊C4D411yescharacteristic
99C2×C11×C4⋊C4C2312yes—
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—22no—
107C2×C11×C22⋊C4D411yescharacteristic
108C2×C11×C22⋊C4D411yescharacteristic
109C2×C42×C11—21no—
110C2×C42×C11—21no—
111C2×C42×C11C2311yescharacteristic
112C2×C42×C11C2311yescharacteristic
113C11×C4⋊C8—22no—
114C11×C4⋊C8—22no—
115C11×#103—24no—
116C11×#102—24no—
117C11×#102—24no—
118C11×#102—24no—
119C11×C22⋊C8—24no—
120C11×#95—21no—
121C11×#95—21no—
122#32913C1111yesmaximal, characteristic, direct product factor, Sylow
123C24×C11—21no—
124C24×C11—22no—
125C24×C11C2×D411yescharacteristic
126C11×#41—28no—
127C11×#41—28no—
128C11×#41—28no—
129C11×#41—28no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11C2×D412yes—
134C2×Q8×C11C2×D412yes—
135C2×Q8×C11#4112yes—
136C2×D4×C11—24no—
137C2×D4×C11—24no—
138C2×D4×C11—24no—
139C2×D4×C11—21no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11—22no—
148C2×D4×C11—44no—
149C2×D4×C11—42no—
150C2×D4×C11—42no—
151C2×D4×C11—82no—
152C2×D4×C11—82no—
153C2×D4×C11—82no—
154C2×D4×C11—82no—
155C2×D4×C11C2×D412yes—
156C2×D4×C11C2×D412yes—
157C2×D4×C11#4112yes—
158C22×C4×C11—24no—
159C22×C4×C11—24no—
160C22×C4×C11—21no—
161C22×C4×C11—24no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—24no—
169C22×C4×C11—24no—
170C22×C4×C11—24no—
171C22×C4×C11—22no—
172C22×C4×C11—82no—
173C22×C4×C11—82no—
174C22×C4×C11—82no—
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D412yes—
181C22×C4×C11#4112yes—
182C22×C4×C11C2411yescharacteristic
183C11×SD16—48no—
184C11×D8—48no—
185C2×C8×C11—22no—
186C2×C8×C11—22no—
187C2×C8×C11—22no—
188C2×C8×C11—22no—
189C2×C8×C11—22no—
190C2×C8×C11—22no—
191C11×C4⋊C4—24no—
192C11×C4⋊C4—24no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—24no—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—22no—
199C11×C4⋊C4—22no—
200C11×C4⋊C4C2×D412yes—
201C11×C4⋊C4C2×D412yes—
202C11×C22⋊C4—24no—
203C11×C22⋊C4—24no—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—44no—
207C11×C22⋊C4—82no—
208C11×C22⋊C4—82no—
209C42×C11—24no—
210C42×C11—24no—
211C42×C11—21no—
212C42×C11—21no—
213C42×C11C2×D412yes—
214C42×C11C2×D412yes—
215C2×#520C2×C1111yescharacteristic, complemented
216C2×#460C2×C1111yescharacteristic, complemented
217C2×#459C2×C1111yescharacteristic, complemented
218C2×#449C2×C1112yescomplemented
219#2619C2×C1111yescharacteristic, complemented
220#1880C2×C1112yescomplemented
221#1879C2×C1112yescomplemented
222#1874C2×C1112yescomplemented
223#1805C2×C1111yescharacteristic, complemented
224#1804C2×C1111yescharacteristic, complemented
225#1798C2×C1111yescharacteristic, complemented
226C23×C11—21no—
227C23×C11—22no—
228C23×C11—22no—
229C23×C11—21no—
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—42no—
236C23×C11—42no—
237C23×C11—42no—
238C23×C11—42no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11—42no—
242C23×C11#12112yes—
243C23×C11C22×D411yescharacteristic
244Q8×C11—22no—
245Q8×C11—22no—
246Q8×C11—22no—
247Q8×C11#12114yes—
248D4×C11—216no—
249D4×C11—22no—
250D4×C11—22no—
251D4×C11—22no—
252D4×C11—42no—
253D4×C11—42no—
254D4×C11—42no—
255D4×C11—42no—
256D4×C11—84no—
257D4×C11—84no—
258D4×C11—88no—
259D4×C11#12114yes—
260C2×C4×C11—216no—
261C2×C4×C11—22no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—21no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—42no—
279C2×C4×C11—42no—
280C2×C4×C11—42no—
281C2×C4×C11—42no—
282C2×C4×C11—42no—
283C2×C4×C11—84no—
284C2×C4×C11—84no—
285C2×C4×C11—84no—
286C2×C4×C11#12012yes—
287C2×C4×C11#12012yes—
288C2×C4×C11#12112yes—
289C2×C4×C11C22×D411yescharacteristic
290C2×C4×C11C22×D411yescharacteristic
291C2×C4×C11C22×D411yescharacteristic
292C2×C4×C11C2×#4111yescharacteristic
293C2×C4×C11C2×#4111yescharacteristic
294C2×C4×C11C2×#4111yescharacteristic
295C8×C11—42no—
296C8×C11—42no—
297C22×#41C22×C1111yescharacteristic
298C22×SD16C22×C1112yes—
299C22×D8C22×C1112yes—
300C2×#127C22×C1111yescharacteristic
301C2×#121C22×C1112yes—
302#520—24no—
303#520—24no—
304C2×C4×Q8C22×C1111yescharacteristic
305C2×C4×Q8C22×C1111yescharacteristic
306C2×C4×D4—21no—
307C2×C4×D4—21no—
308C2×C4×D4C22×C1111yescharacteristic
309C2×C4×D4C22×C1111yescharacteristic
310C2×#117—21no—
311C2×#117C22×C1111yescharacteristic
312C22×C4⋊C4—21no—
313C22×C4⋊C4C22×C1111yescharacteristic
314#460—24no—
315#459—24no—
316#449—28no—
317C2×C4⋊C8C22×C1111yescharacteristic
318C2×C4⋊C8C22×C1111yescharacteristic
319C2×#103C22×C1112yes—
320C2×#102C22×C1112yes—
321C2×#102C22×C1112yes—
322C2×#102C22×C1112yes—
323C2×C22⋊C8C22×C1112yes—
324#394—21no—
325#394—21no—
326#392—21no—
327#392—21no—
328#390C22×C1112yes—
329#382C22×C1111yescharacteristic
330#340C22×C1112yes—
331#340C22×C1112yes—
332#336C22×C1112yes—
333C22×C11—22no—
334C22×C11—24no—
335C22×C11—24no—
336C22×C11—42no—
337C22×C11—44no—
338C22×C11—41no—
339C22×C11—42no—
340C22×C11—41no—
341C22×C11—42no—
342C22×C11—44no—
343C22×C11—82no—
344C22×C11—82no—
345C22×C11—82no—
346C22×C11—82no—
347C22×C11—82no—
348C22×C11—82no—
349C22×C11—82no—
350C22×C11C2×#12011yescharacteristic
351C22×C11C2×#12111yescharacteristic
352C22×C11#52511yescharacteristic
353C22×C11#57612yes—
354C22×C11#57712yes—
355C4×C11—22no—
356C4×C11—24no—
357C4×C11—22no—
358C4×C11—22no—
359C4×C11—41no—
360C4×C11—42no—
361C4×C11—42no—
362C4×C11—41no—
363C4×C11—82no—
364C4×C11C2×#12111yescharacteristic
365C4×C11C2×#12111yescharacteristic
366C4×C11#52511yescharacteristic
367C4×C11#52511yescharacteristic
368C2×#41—22no—
369C2×#41—22no—
370C2×#41—22no—
371C2×#41—22no—
372C2×#41—22no—
373C2×#41D4×C1114yescomplemented
374C22×Q8C23×C1111yescharacteristic
375C22×D4—21no—
376C22×D4—22no—
377C22×D4—21no—
378C22×D4—21no—
379C22×D4C23×C1112yes—
380C22×D4C23×C1111yescharacteristic
381C23×C4—21no—
382C23×C4—21no—
383C23×C4—21no—
384C23×C4—21no—
385C23×C4C23×C1111yescharacteristic
386C2×SD16—24no—
387C2×SD16—24no—
388C2×SD16—24no—
389C2×D8—24no—
390C2×D8—24no—
391C2×D8—24no—
392C22×C8C23×C1112yes—
393C22×C8C23×C1112yes—
394#127—22no—
395#127—22no—
396#121—24no—
397#121—24no—
398C4×Q8—22no—
399C4×Q8—22no—
400C4×Q8—22no—
401C4×Q8D4×C1114yescomplemented
402C4×D4—28no—
403C4×D4—28no—
404C4×D4—22no—
405C4×D4—22no—
406C4×D4—22no—
407C4×D4D4×C1114yescomplemented
408#117—28no—
409#117—22no—
410#117—22no—
411C2×C4⋊C4—28no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4D4×C1111yescharacteristic
418C2×C4⋊C4D4×C1111yescharacteristic
419C2×C4⋊C4C23×C1112yes—
420C2×C4⋊C4C23×C1111yescharacteristic
421C2×C4⋊C4C23×C1111yescharacteristic
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4D4×C1111yescharacteristic
428C2×C22⋊C4D4×C1111yescharacteristic
429C2×C42—21no—
430C2×C42—21no—
431C2×C42C23×C1111yescharacteristic
432C2×C42C23×C1111yescharacteristic
433C4⋊C8—22no—
434C4⋊C8—22no—
435#103—24no—
436#102—24no—
437#102—24no—
438#102—24no—
439C22⋊C8—24no—
440#95—21no—
441#95—21no—
442C2×C11—42no—
443C2×C11—44no—
444C2×C11—162no—
445C2×C11#284711yescharacteristic
446C2×C11#300811yescharacteristic
447C2×C11#301011yescharacteristic
448C2×C11#304512yes—
449C2×C11#311912yes—
450C24—21no—
451C24—22no—
452C24C2×D4×C1111yescharacteristic
453#41—28no—
454#41—28no—
455#41—28no—
456#41—28no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8C2×D4×C1112yes—
461C2×Q8C2×D4×C1112yes—
462C2×Q8C11×#4112yes—
463C2×D4—24no—
464C2×D4—24no—
465C2×D4—24no—
466C2×D4—21no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—44no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4—82no—
479C2×D4—82no—
480C2×D4—82no—
481C2×D4—82no—
482C2×D4C2×D4×C1112yes—
483C2×D4C2×D4×C1112yes—
484C2×D4C11×#4112yes—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—21no—
488C22×C4—24no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—82no—
500C22×C4—82no—
501C22×C4—82no—
502C22×C4C2×D4×C1111yescharacteristic
503C22×C4C2×D4×C1111yescharacteristic
504C22×C4C2×D4×C1111yescharacteristic
505C22×C4C2×D4×C1111yescharacteristic
506C22×C4C2×D4×C1111yescharacteristic
507C22×C4C2×D4×C1112yes—
508C22×C4C11×#4112yes—
509C22×C4C24×C1111yescharacteristic
510SD16—48no—
511D8—48no—
512C2×C8—22no—
513C2×C8—22no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C4⋊C4—24no—
519C4⋊C4—24no—
520C4⋊C4—22no—
521C4⋊C4—24no—
522C4⋊C4—22no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4C2×D4×C1112yes—
528C4⋊C4C2×D4×C1112yes—
529C22⋊C4—24no—
530C22⋊C4—24no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—44no—
534C22⋊C4—82no—
535C22⋊C4—82no—
536C42—24no—
537C42—24no—
538C42—21no—
539C42—21no—
540C42C2×D4×C1112yes—
541C42C2×D4×C1112yes—
542C11#3291311yescharacteristic, direct product factor, Sylow
543C23—21no—
544C23—22no—
545C23—22no—
546C23—21no—
547C23—22no—
548C23—22no—
549C23—22no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23—42no—
554C23—42no—
555C23—42no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23C11×#12112yes—
560C23C22×D4×C1111yescharacteristic
561Q8—22no—
562Q8—22no—
563Q8—22no—
564Q8C11×#12114yes—
565D4—216no—
566D4—22no—
567D4—22no—
568D4—22no—
569D4—42no—
570D4—42no—
571D4—42no—
572D4—42no—
573D4—84no—
574D4—84no—
575D4—88no—
576D4C11×#12114yes—
577C2×C4—216no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—84no—
601C2×C4—84no—
602C2×C4—84no—
603C2×C4C11×#12012yes—
604C2×C4C11×#12012yes—
605C2×C4C11×#12112yes—
606C2×C4C22×D4×C1111yescharacteristic
607C2×C4C22×D4×C1111yescharacteristic
608C2×C4C22×D4×C1111yescharacteristic
609C2×C4C2×C11×#4111yescharacteristic
610C2×C4C2×C11×#4111yescharacteristic
611C2×C4C2×C11×#4111yescharacteristic
612C8—42no—
613C8—42no—
614C22—24no—
615C22—22no—
616C22—24no—
617C22—41no—
618C22—42no—
619C22—41no—
620C22—42no—
621C22—44no—
622C22—42no—
623C22—44no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22—82no—
629C22—82no—
630C22—82no—
631C22C2×C11×#12011yescharacteristic
632C22C2×C11×#12111yescharacteristic
633C22C11×#52511yescharacteristic
634C22C11×#57612yes—
635C22C11×#57712yes—
636C4—22no—
637C4—22no—
638C4—22no—
639C4—24no—
640C4—41no—
641C4—42no—
642C4—42no—
643C4—41no—
644C4—82no—
645C4C2×C11×#12111yescharacteristic
646C4C2×C11×#12111yescharacteristic
647C4C11×#52511yescharacteristic
648C4C11×#52511yescharacteristic
649C2—42no—
650C2—44no—
651C2—162no—
652C2C11×#284711yescharacteristic
653C2C11×#300811yescharacteristic
654C2C11×#301011yescharacteristic
655C2C11×#304512yes—
656C2C11×#311912yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#520C2semidirect
2. C2×C11×#460C2semidirect
3. C2×C11×#459C2semidirect
4. C2×C11×#449C2semidirect
5. C11×#2619C2semidirect
6. C11×#1880C2semidirect
7. C11×#1879C2semidirect
8. C11×#1874C2semidirect
9. C11×#1805C2semidirect
10. C11×#1804C2semidirect
11. C11×#1798C2semidirect
53. C2×C11×#41D4semidirect
81. C4×Q8×C11D4semidirect
87. C4×D4×C11D4semidirect
122. #32913C11direct (N × H)
215. C2×#520C2×C11semidirect
216. C2×#460C2×C11semidirect
217. C2×#459C2×C11semidirect
218. C2×#449C2×C11semidirect
219. #2619C2×C11semidirect
220. #1880C2×C11semidirect
221. #1879C2×C11semidirect
222. #1874C2×C11semidirect
223. #1805C2×C11semidirect
224. #1804C2×C11semidirect
225. #1798C2×C11semidirect
373. C2×#41D4×C11semidirect
401. C4×Q8D4×C11semidirect
407. C4×D4D4×C11semidirect
542. C11#32913direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5202
C2×C11×#4602
C2×C11×#4592
C2×C11×#4492
C11×#26192
C11×#18802
C11×#18792
C11×#18742
C11×#18052
C11×#18042
C11×#17982
#3291311