Finite Group Databasebeta

← C11×#24323 #14601516

Subgroups — C11×#24323 #14601516

Order 2816.

1004 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3503C211yesmaximal, characteristic
2C11×#3078C211yesmaximal, characteristic, complemented
3C4×C11×#137C211yesmaximal, characteristic
4C11×#2567C211yesmaximal, characteristic, complemented
5C11×#2060C212yesmaximal, complemented
6C11×#2028C212yesmaximal, complemented
7C11×#1997C211yesmaximal, characteristic, complemented
8C11×#1986C211yesmaximal, characteristic, complemented
9C11×#1882C212yesmaximal
10C11×#1859C212yesmaximal
11C11×#1806C211yesmaximal, characteristic
12C2×C11×#137C2211yescharacteristic
13Q82×C11—21no—
14C11×#557—21no—
15C11×#554—21no—
16C11×#554—22no—
17D4×Q8×C11—22no—
18D4×Q8×C11—21no—
19C11×#544—22no—
20C11×#544C2212yes—
21C11×#533—21no—
22C11×#533C2211yescharacteristic
23C2×C11×C4⋊Q8—21no—
24C2×C11×C4⋊Q8C2211yescharacteristic
25C11×#520C2212yes—
26C4×C11×#41C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C11×#479—22no—
29C11×#477—21no—
30C11×#475—21no—
31C11×#441—21no—
32C11×#440—21no—
33C4×C11×Q16—21no—
34C4×C11×SD16—21no—
35C11×#428C2211yescharacteristic
36C11×#428C2212yes—
37C11×#423C2211yescharacteristic
38C2×C11×#104C2212yes—
39C11×#419C2212yes—
40C11×#419C2211yescharacteristic
41C11×#417C2211yescharacteristic
42C4×C11×M16C2211yescharacteristic
43C11×#395—22no—
44C11×#391C2212yes—
45C11×#389—22no—
46C11×#384C2212yes—
47C4×C11×C4⋊C4C2211yescharacteristic
48C11×#343C2212yes—
49C11×#343C2212yes—
50C11×#339C2212yes—
51C11×#339C2212yes—
52C11×#339C2212yes—
53C2×C11×#41C2311yescharacteristic
54C22×Q8×C11—22no—
55C22×Q8×C11D412yes—
56C22×Q8×C11C2311yescharacteristic
57C11×#137—22no—
58C11×#137Q814yescomplemented
59C2×C11×Q16—21no—
60C2×C11×SD16—21no—
61C2×C11×M16C2311yescharacteristic
62C2×C11×M16C2312yes—
63C2×C11×M16C2311yescharacteristic
64C11×C4⋊Q8—22no—
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8—24no—
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8—22no—
69C11×C4⋊Q8—21no—
70C11×C4⋊Q8—21no—
71C11×C4⋊Q8—21no—
72C11×C4⋊Q8—21no—
73C11×C4⋊Q8D411yescharacteristic
74C11×C4⋊Q8D411yescharacteristic
75C11×#125—24no—
76C11×#125—22no—
77C11×#125—22no—
78C11×#125D412yes—
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—24no—
82C11×C22⋊Q8—24no—
83C11×C22⋊Q8—21no—
84C11×C22⋊Q8—21no—
85C11×C22⋊Q8—24no—
86C4×Q8×C11—22no—
87C4×Q8×C11—22no—
88C4×Q8×C11—22no—
89C4×Q8×C11—21no—
90C4×Q8×C11—21no—
91C4×Q8×C11—21no—
92C4×Q8×C11—21no—
93C4×Q8×C11—21no—
94C4×Q8×C11—21no—
95C4×Q8×C11D411yescharacteristic
96C4×Q8×C11D411yescharacteristic
97C4×D4×C11—22no—
98C4×D4×C11—21no—
99C4×D4×C11—21no—
100C4×D4×C11—24no—
101C4×D4×C11D411yescharacteristic
102C4×D4×C11D411yescharacteristic
103C11×#117—22no—
104C11×#117—21no—
105C11×#117C2311yescharacteristic
106C11×#117C2312yes—
107C2×C11×C4⋊C4—22no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4—22no—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4—24no—
112C2×C11×C4⋊C4D412yes—
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2312yes—
115C2×C42×C11—21no—
116C2×C42×C11—21no—
117C2×C42×C11C2312yes—
118C2×C42×C11C2311yescharacteristic
119C11×#107—21no—
120C11×#107—22no—
121C11×#106—21no—
122C11×#106—22no—
123C11×C4⋊C8—21no—
124C11×C4⋊C8—21no—
125C11×#104—24no—
126C11×#103—21no—
127C11×#103—21no—
128C11×#103—21no—
129C11×#103—22no—
130C11×#103—22no—
131C11×#102—21no—
132C11×#97—21no—
133C4×C8×C11—21no—
134C11×#95—21no—
135C11×#95—24no—
136#24323C1111yesmaximal, characteristic, direct product factor, Sylow
137C11×#41—21no—
138C11×#41—21no—
139C11×#41C2×Q812yes—
140C11×#41#4112yes—
141C2×Q8×C11—24no—
142C2×Q8×C11—21no—
143C2×Q8×C11—22no—
144C2×Q8×C11—21no—
145C2×Q8×C11—22no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—82no—
152C2×Q8×C11—84no—
153C2×Q8×C11C2×D411yescharacteristic
154C2×Q8×C11C2×Q812yescomplemented
155C2×D4×C11—21no—
156C2×D4×C11C2×D411yescharacteristic
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—22no—
160C22×C4×C11—24no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D414yes—
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2411yescharacteristic
168C11×Q16—24no—
169C11×SD16—24no—
170C11×M16—21no—
171C11×M16—22no—
172C11×M16—21no—
173C11×M16—22no—
174C11×M16—21no—
175C11×M16C2×Q812yescomplemented
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—22no—
179C11×C4⋊C4—24no—
180C11×C4⋊C4—24no—
181C11×C4⋊C4—24no—
182C11×C4⋊C4—24no—
183C11×C4⋊C4—24no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—41no—
197C11×C4⋊C4—41no—
198C11×C4⋊C4—84no—
199C11×C4⋊C4C2×D412yes—
200C11×C4⋊C4C2×D411yescharacteristic
201C11×C4⋊C4C2×D412yes—
202C11×C4⋊C4C2×D411yescharacteristic
203C11×C22⋊C4—24no—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—21no—
206C11×C22⋊C4—21no—
207C11×C22⋊C4—21no—
208C42×C11—24no—
209C42×C11—21no—
210C42×C11—21no—
211C42×C11—21no—
212C42×C11—22no—
213C42×C11—22no—
214C42×C11—22no—
215C42×C11—41no—
216C42×C11—41no—
217C42×C11C2×D411yescharacteristic
218C42×C11C2×D411yescharacteristic
219C42×C11C2×D411yescharacteristic
220C42×C11C2×D411yescharacteristic
221#3503C2×C1111yescharacteristic
222#3078C2×C1111yescharacteristic, complemented
223C4×#137C2×C1111yescharacteristic
224#2567C2×C1111yescharacteristic, complemented
225#2060C2×C1112yescomplemented
226#2028C2×C1112yescomplemented
227#1997C2×C1111yescharacteristic, complemented
228#1986C2×C1111yescharacteristic, complemented
229#1882C2×C1112yes—
230#1859C2×C1112yes—
231#1806C2×C1111yescharacteristic
232C23×C11—21no—
233C23×C11C22×D411yescharacteristic
234Q8×C11—21no—
235Q8×C11—22no—
236Q8×C11—22no—
237Q8×C11—44no—
238Q8×C11—42no—
239Q8×C11—41no—
240Q8×C11—41no—
241Q8×C11—42no—
242Q8×C11—82no—
243Q8×C11—84no—
244Q8×C11C22⋊Q812yes—
245D4×C11—22no—
246D4×C11—22no—
247D4×C11—21no—
248D4×C11C22⋊Q812yes—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—22no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—24no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—41no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—41no—
264C2×C4×C11—42no—
265C2×C4×C11—41no—
266C2×C4×C11—42no—
267C2×C4×C11—44no—
268C2×C4×C11—42no—
269C2×C4×C11—41no—
270C2×C4×C11—84no—
271C2×C4×C11#12011yescharacteristic
272C2×C4×C11#12011yescharacteristic
273C2×C4×C11#12011yescharacteristic
274C2×C4×C11#12011yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C22×Q811yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C112−1+411yescharacteristic
280C2×C4×C112−1+411yescharacteristic
281C8×C11—22no—
282C8×C11—41no—
283C8×C11—42no—
284C2×#137C22×C1111yescharacteristic
285Q82—21no—
286#557—21no—
287#554—21no—
288#554—22no—
289D4×Q8—22no—
290D4×Q8—21no—
291#544—22no—
292#544C22×C1112yes—
293#533—21no—
294#533C22×C1111yescharacteristic
295C2×C4⋊Q8—21no—
296C2×C4⋊Q8C22×C1111yescharacteristic
297#520C22×C1112yes—
298C4×#41C22×C1111yescharacteristic
299C2×C4×Q8C22×C1111yescharacteristic
300#479—22no—
301#477—21no—
302#475—21no—
303#441—21no—
304#440—21no—
305C4×Q16—21no—
306C4×SD16—21no—
307#428C22×C1112yes—
308#428C22×C1111yescharacteristic
309#423C22×C1111yescharacteristic
310C2×#104C22×C1112yes—
311#419C22×C1112yes—
312#419C22×C1111yescharacteristic
313#417C22×C1111yescharacteristic
314C4×M16C22×C1111yescharacteristic
315#395—22no—
316#391C22×C1112yes—
317#389—22no—
318#384C22×C1112yes—
319C4×C4⋊C4C22×C1111yescharacteristic
320#343C22×C1112yes—
321#343C22×C1112yes—
322#339C22×C1112yes—
323#339C22×C1112yes—
324#339C22×C1112yes—
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—22no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11C2×#12011yescharacteristic
331C22×C11#54811yescharacteristic
332C22×C11D4×Q811yescharacteristic
333C4×C11—22no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—44no—
338C4×C11—42no—
339C4×C11—41no—
340C4×C11—42no—
341C4×C11—41no—
342C4×C11—44no—
343C4×C11—42no—
344C4×C11—81no—
345C4×C11#45612yes—
346C4×C11C2×C22⋊Q811yescharacteristic
347C4×C11#53611yescharacteristic
348C4×C11#54811yescharacteristic
349C4×C11D4×Q811yescharacteristic
350C2×#41C23×C1111yescharacteristic
351C22×Q8—22no—
352C22×Q8D4×C1112yes—
353C22×Q8C23×C1111yescharacteristic
354#137—22no—
355#137Q8×C1114yescomplemented
356C2×Q16—21no—
357C2×SD16—21no—
358C2×M16C23×C1111yescharacteristic
359C2×M16C23×C1112yes—
360C2×M16C23×C1111yescharacteristic
361C4⋊Q8—22no—
362C4⋊Q8—22no—
363C4⋊Q8—24no—
364C4⋊Q8—22no—
365C4⋊Q8—22no—
366C4⋊Q8—21no—
367C4⋊Q8—21no—
368C4⋊Q8—21no—
369C4⋊Q8—21no—
370C4⋊Q8D4×C1111yescharacteristic
371C4⋊Q8D4×C1111yescharacteristic
372#125—24no—
373#125—22no—
374#125—22no—
375#125D4×C1112yes—
376C22⋊Q8—22no—
377C22⋊Q8—22no—
378C22⋊Q8—24no—
379C22⋊Q8—24no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382C22⋊Q8—24no—
383C4×Q8—22no—
384C4×Q8—22no—
385C4×Q8—22no—
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8D4×C1111yescharacteristic
393C4×Q8D4×C1111yescharacteristic
394C4×D4—22no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—24no—
398C4×D4D4×C1111yescharacteristic
399C4×D4D4×C1111yescharacteristic
400#117—22no—
401#117—21no—
402#117C23×C1111yescharacteristic
403#117C23×C1112yes—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4D4×C1112yes—
410C2×C4⋊C4C23×C1111yescharacteristic
411C2×C4⋊C4C23×C1112yes—
412C2×C42—21no—
413C2×C42—21no—
414C2×C42C23×C1112yes—
415C2×C42C23×C1111yescharacteristic
416#107—21no—
417#107—22no—
418#106—21no—
419#106—22no—
420C4⋊C8—21no—
421C4⋊C8—21no—
422#104—24no—
423#103—21no—
424#103—21no—
425#103—21no—
426#103—22no—
427#103—22no—
428#102—21no—
429#97—21no—
430C4×C8—21no—
431#95—21no—
432#95—24no—
433C2×C11—21no—
434C2×C11—21no—
435C2×C11—42no—
436C2×C11#240911yescharacteristic
437C2×C11C2×#45611yescharacteristic
438C2×C11#301911yescharacteristic
439#41—21no—
440#41—21no—
441#41C2×Q8×C1112yes—
442#41C11×#4112yes—
443C2×Q8—24no—
444C2×Q8—21no—
445C2×Q8—22no—
446C2×Q8—21no—
447C2×Q8—22no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—82no—
454C2×Q8—84no—
455C2×Q8C2×D4×C1111yescharacteristic
456C2×Q8C2×Q8×C1112yescomplemented
457C2×D4—21no—
458C2×D4C2×D4×C1111yescharacteristic
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4C2×D4×C1111yescharacteristic
467C22×C4C2×D4×C1114yes—
468C22×C4C2×D4×C1111yescharacteristic
469C22×C4C24×C1111yescharacteristic
470Q16—24no—
471SD16—24no—
472M16—21no—
473M16—22no—
474M16—21no—
475M16—21no—
476M16—22no—
477M16C2×Q8×C1112yescomplemented
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—22no—
481C4⋊C4—24no—
482C4⋊C4—24no—
483C4⋊C4—24no—
484C4⋊C4—24no—
485C4⋊C4—24no—
486C4⋊C4—21no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—84no—
501C4⋊C4C2×D4×C1112yes—
502C4⋊C4C2×D4×C1111yescharacteristic
503C4⋊C4C2×D4×C1112yes—
504C4⋊C4C2×D4×C1111yescharacteristic
505C22⋊C4—24no—
506C22⋊C4—22no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C42—24no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—22no—
515C42—22no—
516C42—22no—
517C42—41no—
518C42—41no—
519C42C2×D4×C1111yescharacteristic
520C42C2×D4×C1111yescharacteristic
521C42C2×D4×C1111yescharacteristic
522C42C2×D4×C1111yescharacteristic
523C11#2432311yescharacteristic, direct product factor, Sylow
524C23—21no—
525C23C22×D4×C1111yescharacteristic
526Q8—21no—
527Q8—22no—
528Q8—22no—
529Q8—44no—
530Q8—42no—
531Q8—41no—
532Q8—41no—
533Q8—42no—
534Q8—82no—
535Q8—84no—
536Q8C11×C22⋊Q812yes—
537D4—22no—
538D4—22no—
539D4—21no—
540D4C11×C22⋊Q812yes—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—44no—
560C2×C4—42no—
561C2×C4—41no—
562C2×C4—84no—
563C2×C4C11×#12011yescharacteristic
564C2×C4C11×#12011yescharacteristic
565C2×C4C11×#12011yescharacteristic
566C2×C4C11×#12011yescharacteristic
567C2×C4C22×D4×C1111yescharacteristic
568C2×C4C22×D4×C1111yescharacteristic
569C2×C4C22×Q8×C1111yescharacteristic
570C2×C4C2×C11×#4111yescharacteristic
571C2×C4C11×2−1+411yescharacteristic
572C2×C4C11×2−1+411yescharacteristic
573C8—22no—
574C8—41no—
575C8—42no—
576C22—21no—
577C22—21no—
578C22—22no—
579C22—41no—
580C22—41no—
581C22C2×C11×#12011yescharacteristic
582C22C11×#54811yescharacteristic
583C22D4×Q8×C1111yescharacteristic
584C4—22no—
585C4—21no—
586C4—21no—
587C4—21no—
588C4—44no—
589C4—42no—
590C4—41no—
591C4—42no—
592C4—41no—
593C4—44no—
594C4—42no—
595C4—81no—
596C4C11×#45612yes—
597C4C2×C11×C22⋊Q811yescharacteristic
598C4C11×#53611yescharacteristic
599C4C11×#54811yescharacteristic
600C4D4×Q8×C1111yescharacteristic
601C2—21no—
602C2—21no—
603C2—42no—
604C2C11×#240911yescharacteristic
605C2C2×C11×#45611yescharacteristic
606C2C11×#301911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3078C2semidirect
4. C11×#2567C2semidirect
5. C11×#2060C2semidirect
6. C11×#2028C2semidirect
7. C11×#1997C2semidirect
8. C11×#1986C2semidirect
58. C11×#137Q8semidirect
136. #24323C11direct (N × H)
154. C2×Q8×C11C2×Q8semidirect
175. C11×M16C2×Q8semidirect
222. #3078C2×C11semidirect
224. #2567C2×C11semidirect
225. #2060C2×C11semidirect
226. #2028C2×C11semidirect
227. #1997C2×C11semidirect
228. #1986C2×C11semidirect
355. #137Q8×C11semidirect
456. C2×Q8C2×Q8×C11semidirect
477. M16C2×Q8×C11semidirect
523. C11#24323direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35032
C11×#30782
C4×C11×#1372
C11×#25672
C11×#20602
C11×#20282
C11×#19972
C11×#19862
C11×#18822
C11×#18592
C11×#18062
#2432311