Finite Group Databasebeta

← C11×#24322 #14601515

Subgroups — C11×#24322 #14601515

Order 2816.

988 conjugacy classes of subgroups.

The subgroup lattice has 606 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×#2568C211yesmaximal, characteristic, complemented
5C11×#2061C212yesmaximal, complemented
6C11×#2028C212yesmaximal, complemented
7C11×#1997C211yesmaximal, characteristic, complemented
8C11×#1986C211yesmaximal, characteristic, complemented
9C11×#1882C212yesmaximal
10C11×#1860C212yesmaximal
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×#400—22no—
44C11×#391—22no—
45C11×#391C2212yes—
46C11×#382C2212yes—
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—22no—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4D412yes—
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2312yes—
114C2×C42×C11—21no—
115C2×C42×C11—21no—
116C2×C42×C11C2312yes—
117C2×C42×C11C2311yescharacteristic
118C11×#107—21no—
119C11×#107—22no—
120C11×#106—21no—
121C11×#106—22no—
122C11×C4⋊C8—21no—
123C11×C4⋊C8—21no—
124C11×#104—24no—
125C11×#103—21no—
126C11×#103—21no—
127C11×#103—21no—
128C11×#103—22no—
129C11×#103—22no—
130C11×#102—21no—
131C11×#97—21no—
132C4×C8×C11—21no—
133C11×#95—21no—
134C11×#95—24no—
135C11×#95—24no—
136#24322C1111yesmaximal, 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—44no—
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—24no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—22no—
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—21no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—42no—
196C11×C4⋊C4—41no—
197C11×C4⋊C4—41no—
198C11×C4⋊C4C2×D412yes—
199C11×C4⋊C4C2×D411yescharacteristic
200C11×C4⋊C4C2×D412yes—
201C11×C4⋊C4C2×D411yescharacteristic
202C11×C22⋊C4—24no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—21no—
205C11×C22⋊C4—21no—
206C11×C22⋊C4—21no—
207C42×C11—24no—
208C42×C11—21no—
209C42×C11—21no—
210C42×C11—21no—
211C42×C11—22no—
212C42×C11—22no—
213C42×C11—22no—
214C42×C11—41no—
215C42×C11—41no—
216C42×C11C2×D411yescharacteristic
217C42×C11C2×D411yescharacteristic
218C42×C11C2×D411yescharacteristic
219C42×C11C2×D411yescharacteristic
220#3503C2×C1111yescharacteristic
221#3078C2×C1111yescharacteristic, complemented
222C4×#137C2×C1111yescharacteristic
223#2568C2×C1111yescharacteristic, complemented
224#2061C2×C1112yescomplemented
225#2028C2×C1112yescomplemented
226#1997C2×C1111yescharacteristic, complemented
227#1986C2×C1111yescharacteristic, complemented
228#1882C2×C1112yes—
229#1860C2×C1112yes—
230#1806C2×C1111yescharacteristic
231C23×C11—21no—
232C23×C11C22×D411yescharacteristic
233Q8×C11—21no—
234Q8×C11—22no—
235Q8×C11—22no—
236Q8×C11—42no—
237Q8×C11—41no—
238Q8×C11—41no—
239Q8×C11—44no—
240Q8×C11—42no—
241Q8×C11—82no—
242Q8×C11—84no—
243Q8×C11C22⋊Q812yes—
244D4×C11—22no—
245D4×C11—22no—
246D4×C11—21no—
247D4×C11C22⋊Q812yes—
248C2×C4×C11—21no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—24no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—41no—
259C2×C4×C11—42no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—42no—
263C2×C4×C11—44no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—41no—
268C2×C4×C11—42no—
269C2×C4×C11—84no—
270C2×C4×C11#12011yescharacteristic
271C2×C4×C11#12011yescharacteristic
272C2×C4×C11#12011yescharacteristic
273C2×C4×C11#12011yescharacteristic
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C22×Q811yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C112−1+411yescharacteristic
279C2×C4×C112−1+411yescharacteristic
280C8×C11—22no—
281C8×C11—41no—
282C8×C11—42no—
283C2×#137C22×C1111yescharacteristic
284Q82—21no—
285#557—21no—
286#554—21no—
287#554—22no—
288D4×Q8—22no—
289D4×Q8—21no—
290#544—22no—
291#544C22×C1112yes—
292#533—21no—
293#533C22×C1111yescharacteristic
294C2×C4⋊Q8—21no—
295C2×C4⋊Q8C22×C1111yescharacteristic
296#520C22×C1112yes—
297C4×#41C22×C1111yescharacteristic
298C2×C4×Q8C22×C1111yescharacteristic
299#479—22no—
300#477—21no—
301#475—21no—
302#441—21no—
303#440—21no—
304C4×Q16—21no—
305C4×SD16—21no—
306#428C22×C1112yes—
307#428C22×C1111yescharacteristic
308#423C22×C1111yescharacteristic
309C2×#104C22×C1112yes—
310#419C22×C1112yes—
311#419C22×C1111yescharacteristic
312#417C22×C1111yescharacteristic
313C4×M16C22×C1111yescharacteristic
314#400—22no—
315#391—22no—
316#391C22×C1112yes—
317#382C22×C1112yes—
318C4×C4⋊C4C22×C1111yescharacteristic
319#343C22×C1112yes—
320#343C22×C1112yes—
321#339C22×C1112yes—
322#339C22×C1112yes—
323#339C22×C1112yes—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—22no—
327C22×C11—41no—
328C22×C11—41no—
329C22×C11C2×#12011yescharacteristic
330C22×C11#54811yescharacteristic
331C22×C11D4×Q811yescharacteristic
332C4×C11—22no—
333C4×C11—21no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—42no—
337C4×C11—41no—
338C4×C11—44no—
339C4×C11—42no—
340C4×C11—41no—
341C4×C11—42no—
342C4×C11—82no—
343C4×C11—81no—
344C4×C11#45512yes—
345C4×C11C2×C22⋊Q811yescharacteristic
346C4×C11#53611yescharacteristic
347C4×C11#54811yescharacteristic
348C4×C11D4×Q811yescharacteristic
349C2×#41C23×C1111yescharacteristic
350C22×Q8—22no—
351C22×Q8D4×C1112yes—
352C22×Q8C23×C1111yescharacteristic
353#137—22no—
354#137Q8×C1114yescomplemented
355C2×Q16—21no—
356C2×SD16—21no—
357C2×M16C23×C1111yescharacteristic
358C2×M16C23×C1112yes—
359C2×M16C23×C1111yescharacteristic
360C4⋊Q8—22no—
361C4⋊Q8—22no—
362C4⋊Q8—24no—
363C4⋊Q8—22no—
364C4⋊Q8—22no—
365C4⋊Q8—21no—
366C4⋊Q8—21no—
367C4⋊Q8—21no—
368C4⋊Q8—21no—
369C4⋊Q8D4×C1111yescharacteristic
370C4⋊Q8D4×C1111yescharacteristic
371#125—24no—
372#125—22no—
373#125—22no—
374#125D4×C1112yes—
375C22⋊Q8—22no—
376C22⋊Q8—22no—
377C22⋊Q8—24no—
378C22⋊Q8—24no—
379C22⋊Q8—21no—
380C22⋊Q8—21no—
381C22⋊Q8—24no—
382C4×Q8—22no—
383C4×Q8—22no—
384C4×Q8—22no—
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8D4×C1111yescharacteristic
392C4×Q8D4×C1111yescharacteristic
393C4×D4—22no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—24no—
397C4×D4D4×C1111yescharacteristic
398C4×D4D4×C1111yescharacteristic
399#117—22no—
400#117—21no—
401#117C23×C1111yescharacteristic
402#117C23×C1112yes—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4D4×C1112yes—
408C2×C4⋊C4C23×C1111yescharacteristic
409C2×C4⋊C4C23×C1112yes—
410C2×C42—21no—
411C2×C42—21no—
412C2×C42C23×C1112yes—
413C2×C42C23×C1111yescharacteristic
414#107—21no—
415#107—22no—
416#106—21no—
417#106—22no—
418C4⋊C8—21no—
419C4⋊C8—21no—
420#104—24no—
421#103—21no—
422#103—21no—
423#103—21no—
424#103—22no—
425#103—22no—
426#102—21no—
427#97—21no—
428C4×C8—21no—
429#95—21no—
430#95—24no—
431#95—24no—
432C2×C11—21no—
433C2×C11—21no—
434C2×C11—42no—
435C2×C11#240911yescharacteristic
436C2×C11C2×#45511yescharacteristic
437C2×C11#302011yescharacteristic
438#41—21no—
439#41—21no—
440#41C2×Q8×C1112yes—
441#41C11×#4112yes—
442C2×Q8—24no—
443C2×Q8—21no—
444C2×Q8—22no—
445C2×Q8—21no—
446C2×Q8—22no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—44no—
453C2×Q8—84no—
454C2×Q8C2×D4×C1111yescharacteristic
455C2×Q8C2×Q8×C1112yescomplemented
456C2×D4—21no—
457C2×D4C2×D4×C1111yescharacteristic
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—24no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4C2×D4×C1111yescharacteristic
466C22×C4C2×D4×C1114yes—
467C22×C4C2×D4×C1111yescharacteristic
468C22×C4C24×C1111yescharacteristic
469Q16—24no—
470SD16—24no—
471M16—21no—
472M16—22no—
473M16—21no—
474M16—21no—
475M16—22no—
476M16C2×Q8×C1112yescomplemented
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—22no—
480C4⋊C4—24no—
481C4⋊C4—24no—
482C4⋊C4—24no—
483C4⋊C4—24no—
484C4⋊C4—21no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—42no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4C2×D4×C1112yes—
500C4⋊C4C2×D4×C1111yescharacteristic
501C4⋊C4C2×D4×C1112yes—
502C4⋊C4C2×D4×C1111yescharacteristic
503C22⋊C4—24no—
504C22⋊C4—22no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C42—24no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—22no—
513C42—22no—
514C42—22no—
515C42—41no—
516C42—41no—
517C42C2×D4×C1111yescharacteristic
518C42C2×D4×C1111yescharacteristic
519C42C2×D4×C1111yescharacteristic
520C42C2×D4×C1111yescharacteristic
521C11#2432211yescharacteristic, direct product factor, Sylow
522C23—21no—
523C23C22×D4×C1111yescharacteristic
524Q8—21no—
525Q8—22no—
526Q8—22no—
527Q8—42no—
528Q8—41no—
529Q8—41no—
530Q8—44no—
531Q8—42no—
532Q8—82no—
533Q8—84no—
534Q8C11×C22⋊Q812yes—
535D4—22no—
536D4—22no—
537D4—21no—
538D4C11×C22⋊Q812yes—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—44no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—84no—
561C2×C4C11×#12011yescharacteristic
562C2×C4C11×#12011yescharacteristic
563C2×C4C11×#12011yescharacteristic
564C2×C4C11×#12011yescharacteristic
565C2×C4C22×D4×C1111yescharacteristic
566C2×C4C22×D4×C1111yescharacteristic
567C2×C4C22×Q8×C1111yescharacteristic
568C2×C4C2×C11×#4111yescharacteristic
569C2×C4C11×2−1+411yescharacteristic
570C2×C4C11×2−1+411yescharacteristic
571C8—22no—
572C8—41no—
573C8—42no—
574C22—21no—
575C22—21no—
576C22—22no—
577C22—41no—
578C22—41no—
579C22C2×C11×#12011yescharacteristic
580C22C11×#54811yescharacteristic
581C22D4×Q8×C1111yescharacteristic
582C4—22no—
583C4—21no—
584C4—21no—
585C4—21no—
586C4—42no—
587C4—41no—
588C4—44no—
589C4—42no—
590C4—41no—
591C4—42no—
592C4—82no—
593C4—81no—
594C4C11×#45512yes—
595C4C2×C11×C22⋊Q811yescharacteristic
596C4C11×#53611yescharacteristic
597C4C11×#54811yescharacteristic
598C4D4×Q8×C1111yescharacteristic
599C2—21no—
600C2—21no—
601C2—42no—
602C2C11×#240911yescharacteristic
603C2C2×C11×#45511yescharacteristic
604C2C11×#302011yescharacteristic
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×#2568C2semidirect
5. C11×#2061C2semidirect
6. C11×#2028C2semidirect
7. C11×#1997C2semidirect
8. C11×#1986C2semidirect
58. C11×#137Q8semidirect
136. #24322C11direct (N × H)
154. C2×Q8×C11C2×Q8semidirect
175. C11×M16C2×Q8semidirect
221. #3078C2×C11semidirect
223. #2568C2×C11semidirect
224. #2061C2×C11semidirect
225. #2028C2×C11semidirect
226. #1997C2×C11semidirect
227. #1986C2×C11semidirect
354. #137Q8×C11semidirect
455. C2×Q8C2×Q8×C11semidirect
476. M16C2×Q8×C11semidirect
521. C11#24322direct (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×#25682
C11×#20612
C11×#20282
C11×#19972
C11×#19862
C11×#18822
C11×#18602
C11×#18062
#2432211