Finite Group Databasebeta

← C11×#24151 #14601344

Subgroups — C11×#24151 #14601344

Order 2816.

1198 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#533C211yesmaximal, characteristic, complemented
2C2×C11×#476C211yesmaximal, characteristic, complemented
3C2×C11×#461C211yesmaximal, characteristic, complemented
4C4×C11×#121C211yesmaximal, characteristic
5C11×#2035C212yesmaximal, complemented
6C11×#2000C212yesmaximal
7C11×#1987C211yesmaximal, characteristic, complemented
8C11×#1981C211yesmaximal, characteristic, complemented
9C11×#1880C212yesmaximal, complemented
10C11×#1865C212yesmaximal, complemented
11C11×#1797C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2212yes—
13C11×#533—24no—
14C11×#533—24no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#125—21no—
18C2×C11×C22⋊Q8—21no—
19C2×C11×C22⋊Q8C2212yes—
20C2×C11×#121C2211yescharacteristic
21C2×C4×Q8×C11—21no—
22C2×C4×Q8×C11C2212yes—
23C2×C4×D4×C11—21no—
24C2×C4×D4×C11C2211yescharacteristic
25C2×C11×#117—21no—
26C22×C42×C11C2211yescharacteristic
27C11×#476—24no—
28C11×#461—24no—
29C2×C11×#106C2212yes—
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×C4⋊C8C2211yescharacteristic
32C2×C11×#103C2212yes—
33C2×C11×#103C2212yes—
34C2×C11×#103C2212yes—
35C2×C11×#102C2212yes—
36C2×C11×C22⋊C8C2212yes—
37C11×#390C2211yescharacteristic
38C11×#389C2211yescharacteristic
39C11×#388—21no—
40C11×#386—21no—
41C11×#380C2211yescharacteristic
42C4×C11×C4⋊C4C2211yescharacteristic
43C4×C11×C22⋊C4—21no—
44C11×#340C2212yes—
45C11×#340C2212yes—
46C11×#336C2212yes—
47C22×Q8×C11—21no—
48C22×Q8×C11C2312yes—
49C22×D4×C11—21no—
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11D411yescharacteristic
53C23×C4×C11D411yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C2×C11×SD16—24no—
56C2×C11×SD16—24no—
57C2×C11×SD16—42no—
58C22×C8×C11C2312yes—
59C22×C8×C11C2312yes—
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8D414yescomplemented
63C11×C4⋊Q8D414yescomplemented
64C11×#125—28no—
65C11×C22⋊Q8—28no—
66C11×C22⋊Q8—24no—
67C11×C22⋊Q8—24no—
68C11×#121—22no—
69C11×#121—22no—
70C4×Q8×C11—28no—
71C4×Q8×C11—24no—
72C4×Q8×C11—24no—
73C4×D4×C11—22no—
74C4×D4×C11—22no—
75C4×D4×C11—44no—
76C11×#117—28no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C42×C11—22no—
94C2×C42×C11—22no—
95C2×C42×C11—22no—
96C2×C42×C11—21no—
97C2×C42×C11D411yescharacteristic
98C2×C42×C11D411yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2311yescharacteristic
101C11×#106—24no—
102C11×C4⋊C8—22no—
103C11×C4⋊C8—22no—
104C11×#103—24no—
105C11×#103—24no—
106C11×#103—42no—
107C11×#102—24no—
108C11×C22⋊C8—42no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112#24151C1111yesmaximal, characteristic, direct product factor, Sylow
113C24×C11—21no—
114C24×C11C2×D411yescharacteristic
115C2×Q8×C11—24no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11—42no—
122C2×Q8×C11—42no—
123C2×Q8×C11C2×D414yes—
124C2×D4×C11—24no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—42no—
131C2×D4×C11—42no—
132C2×D4×C11#4112yes—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—41no—
148C22×C4×C11—41no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11—42no—
152C22×C4×C11SD1614yescomplemented
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2411yescharacteristic
159C11×SD16—48no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C11×C4⋊C4—28no—
167C11×C4⋊C4—28no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4—24no—
170C11×C4⋊C4—24no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4C2×D414yes—
179C11×C4⋊C4#4112yes—
180C11×C22⋊C4—28no—
181C11×C22⋊C4—24no—
182C11×C22⋊C4—42no—
183C11×C22⋊C4—42no—
184C11×C22⋊C4—42no—
185C11×C22⋊C4—42no—
186C42×C11—28no—
187C42×C11—22no—
188C42×C11—22no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—42no—
192C42×C11C2×D412yes—
193C42×C11C2×D412yes—
194C2×#533C2×C1111yescharacteristic, complemented
195C2×#476C2×C1111yescharacteristic, complemented
196C2×#461C2×C1111yescharacteristic, complemented
197C4×#121C2×C1111yescharacteristic
198#2035C2×C1112yescomplemented
199#2000C2×C1112yes—
200#1987C2×C1111yescharacteristic, complemented
201#1981C2×C1111yescharacteristic, complemented
202#1880C2×C1112yescomplemented
203#1865C2×C1112yescomplemented
204#1797C2×C1111yescharacteristic, complemented
205C23×C11—21no—
206C23×C11—21no—
207C23×C11—21no—
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—22no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11C2×SD1612yes—
219C23×C11C22×D411yescharacteristic
220Q8×C11—24no—
221Q8×C11—24no—
222Q8×C11—48no—
223Q8×C11—42no—
224Q8×C11—42no—
225D4×C11—22no—
226D4×C11—22no—
227D4×C11—48no—
228D4×C11—41no—
229D4×C11—41no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—28no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—44no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—84no—
262C2×C4×C11#12012yes—
263C2×C4×C11#12012yes—
264C2×C4×C11C2×SD1612yes—
265C2×C4×C11C2×SD1612yes—
266C2×C4×C11#13712yes—
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11H(5,𝔽2)11yescharacteristic
272C2×C4×C112−1+411yescharacteristic
273C8×C11—42no—
274C8×C11—42no—
275C22×SD16C22×C1112yes—
276#533—24no—
277#533—24no—
278C2×C4⋊Q8C22×C1111yescharacteristic
279C2×C4⋊Q8C22×C1111yescharacteristic
280C2×#125—21no—
281C2×C22⋊Q8—21no—
282C2×C22⋊Q8C22×C1112yes—
283C2×#121C22×C1111yescharacteristic
284C2×C4×Q8—21no—
285C2×C4×Q8C22×C1112yes—
286C2×C4×D4—21no—
287C2×C4×D4C22×C1111yescharacteristic
288C2×#117—21no—
289C22×C42C22×C1111yescharacteristic
290#476—24no—
291#461—24no—
292C2×#106C22×C1112yes—
293C2×C4⋊C8C22×C1111yescharacteristic
294C2×C4⋊C8C22×C1111yescharacteristic
295C2×#103C22×C1112yes—
296C2×#103C22×C1112yes—
297C2×#103C22×C1112yes—
298C2×#102C22×C1112yes—
299C2×C22⋊C8C22×C1112yes—
300#390C22×C1111yescharacteristic
301#389C22×C1111yescharacteristic
302#388—21no—
303#386—21no—
304#380C22×C1111yescharacteristic
305C4×C4⋊C4C22×C1111yescharacteristic
306C4×C22⋊C4—21no—
307#340C22×C1112yes—
308#340C22×C1112yes—
309#336C22×C1112yes—
310C22×C11—22no—
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—41no—
314C22×C11—41no—
315C22×C11—41no—
316C22×C11—41no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—42no—
320C22×C11—81no—
321C22×C11—81no—
322C22×C11—81no—
323C22×C11—81no—
324C22×C11C2×#12011yescharacteristic
325C22×C11#52511yescharacteristic
326C22×C11#53711yescharacteristic
327C22×C11C22×SD1611yescharacteristic
328C22×C11C2×#13711yescharacteristic
329C22×C11#57511yescharacteristic
330C22×C11#57511yescharacteristic
331C4×C11—22no—
332C4×C11—22no—
333C4×C11—42no—
334C4×C11—41no—
335C4×C11—44no—
336C4×C11—41no—
337C4×C11—44no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11#44814yes—
341C4×C11#54611yescharacteristic
342C4×C11#54711yescharacteristic
343C4×C11#54811yescharacteristic
344C4×C11#55011yescharacteristic
345C22×Q8—21no—
346C22×Q8C23×C1112yes—
347C22×D4—21no—
348C22×D4C23×C1111yescharacteristic
349C23×C4—21no—
350C23×C4D4×C1111yescharacteristic
351C23×C4D4×C1111yescharacteristic
352C23×C4C23×C1111yescharacteristic
353C2×SD16—24no—
354C2×SD16—24no—
355C2×SD16—42no—
356C22×C8C23×C1112yes—
357C22×C8C23×C1112yes—
358C4⋊Q8—22no—
359C4⋊Q8—22no—
360C4⋊Q8D4×C1114yescomplemented
361C4⋊Q8D4×C1114yescomplemented
362#125—28no—
363C22⋊Q8—28no—
364C22⋊Q8—24no—
365C22⋊Q8—24no—
366#121—22no—
367#121—22no—
368C4×Q8—28no—
369C4×Q8—24no—
370C4×Q8—24no—
371C4×D4—22no—
372C4×D4—22no—
373C4×D4—44no—
374#117—28no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4C23×C1111yescharacteristic
382C2×C4⋊C4C23×C1111yescharacteristic
383C2×C4⋊C4C23×C1112yes—
384C2×C4⋊C4C23×C1111yescharacteristic
385C2×C22⋊C4—22no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—21no—
395C2×C42D4×C1111yescharacteristic
396C2×C42D4×C1111yescharacteristic
397C2×C42C23×C1111yescharacteristic
398C2×C42C23×C1111yescharacteristic
399#106—24no—
400C4⋊C8—22no—
401C4⋊C8—22no—
402#103—24no—
403#103—24no—
404#103—42no—
405#102—24no—
406C22⋊C8—42no—
407#95—21no—
408#95—21no—
409#95—21no—
410C2×C11—42no—
411C2×C11—82no—
412C2×C11#240711yescharacteristic
413C2×C11C2×#44811yescharacteristic
414C2×C11#300511yescharacteristic
415C2×C11#310111yescharacteristic
416C2×C11#311611yescharacteristic
417C2×C11#324611yescharacteristic
418C2×C11#325211yescharacteristic
419C24—21no—
420C24C2×D4×C1111yescharacteristic
421C2×Q8—24no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8—22no—
426C2×Q8—22no—
427C2×Q8—42no—
428C2×Q8—42no—
429C2×Q8C2×D4×C1114yes—
430C2×D4—24no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—42no—
437C2×D4—42no—
438C2×D4C11×#4112yes—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4C11×SD1614yescomplemented
459C22×C4C2×D4×C1111yescharacteristic
460C22×C4C2×D4×C1111yescharacteristic
461C22×C4C2×D4×C1111yescharacteristic
462C22×C4C2×D4×C1111yescharacteristic
463C22×C4C2×D4×C1111yescharacteristic
464C22×C4C24×C1111yescharacteristic
465SD16—48no—
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C4⋊C4—28no—
473C4⋊C4—28no—
474C4⋊C4—24no—
475C4⋊C4—24no—
476C4⋊C4—24no—
477C4⋊C4—22no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—42no—
484C4⋊C4C2×D4×C1114yes—
485C4⋊C4C11×#4112yes—
486C22⋊C4—28no—
487C22⋊C4—24no—
488C22⋊C4—42no—
489C22⋊C4—42no—
490C22⋊C4—42no—
491C22⋊C4—42no—
492C42—28no—
493C42—22no—
494C42—22no—
495C42—21no—
496C42—21no—
497C42—42no—
498C42C2×D4×C1112yes—
499C42C2×D4×C1112yes—
500C11#2415111yescharacteristic, direct product factor, Sylow
501C23—21no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—21no—
507C23—22no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23C2×C11×SD1612yes—
515C23C22×D4×C1111yescharacteristic
516Q8—24no—
517Q8—24no—
518Q8—48no—
519Q8—42no—
520Q8—42no—
521D4—22no—
522D4—22no—
523D4—48no—
524D4—41no—
525D4—41no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—28no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—44no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—84no—
558C2×C4C11×#12012yes—
559C2×C4C11×#12012yes—
560C2×C4C2×C11×SD1612yes—
561C2×C4C2×C11×SD1612yes—
562C2×C4C11×#13712yes—
563C2×C4C22×D4×C1111yescharacteristic
564C2×C4C22×D4×C1111yescharacteristic
565C2×C4C2×C11×#4111yescharacteristic
566C2×C4C2×C11×#4111yescharacteristic
567C2×C4C11×H(5,𝔽2)11yescharacteristic
568C2×C4C11×2−1+411yescharacteristic
569C8—42no—
570C8—42no—
571C22—22no—
572C22—22no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22C2×C11×#12011yescharacteristic
586C22C11×#52511yescharacteristic
587C22C11×#53711yescharacteristic
588C22C22×C11×SD1611yescharacteristic
589C22C2×C11×#13711yescharacteristic
590C22C11×#57511yescharacteristic
591C22C11×#57511yescharacteristic
592C4—22no—
593C4—22no—
594C4—41no—
595C4—44no—
596C4—41no—
597C4—44no—
598C4—42no—
599C4—81no—
600C4—81no—
601C4C11×#44814yes—
602C4C11×#54611yescharacteristic
603C4C11×#54711yescharacteristic
604C4C11×#54811yescharacteristic
605C4C11×#55011yescharacteristic
606C2—42no—
607C2—82no—
608C2C11×#240711yescharacteristic
609C2C2×C11×#44811yescharacteristic
610C2C11×#300511yescharacteristic
611C2C11×#310111yescharacteristic
612C2C11×#311611yescharacteristic
613C2C11×#324611yescharacteristic
614C2C11×#325211yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#533C2semidirect
2. C2×C11×#476C2semidirect
3. C2×C11×#461C2semidirect
5. C11×#2035C2semidirect
7. C11×#1987C2semidirect
8. C11×#1981C2semidirect
9. C11×#1880C2semidirect
10. C11×#1865C2semidirect
11. C11×#1797C2semidirect
62. C11×C4⋊Q8D4semidirect
63. C11×C4⋊Q8D4semidirect
112. #24151C11direct (N × H)
152. C22×C4×C11SD16semidirect
194. C2×#533C2×C11semidirect
195. C2×#476C2×C11semidirect
196. C2×#461C2×C11semidirect
198. #2035C2×C11semidirect
200. #1987C2×C11semidirect
201. #1981C2×C11semidirect
202. #1880C2×C11semidirect
203. #1865C2×C11semidirect
204. #1797C2×C11semidirect
360. C4⋊Q8D4×C11semidirect
361. C4⋊Q8D4×C11semidirect
458. C22×C4C11×SD16semidirect
500. C11#24151direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5332
C2×C11×#4762
C2×C11×#4612
C4×C11×#1212
C11×#20352
C11×#20002
C11×#19872
C11×#19812
C11×#18802
C11×#18652
C11×#17972
#2415111