Finite Group Databasebeta

← C11×#16305 #14593498

Subgroups — C11×#16305 #14593498

Order 2816.

1618 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#398C212yesmaximal, complemented
2C2×C11×#396C212yesmaximal
3C2×C11×#380C212yesmaximal
4C11×#1444C212yesmaximal, complemented
5C11×#1444C212yesmaximal, complemented
6C11×#1441C212yesmaximal, complemented
7C11×#1439C211yesmaximal, characteristic
8C11×#1439C211yesmaximal, characteristic
9C11×C22⋊#95C211yesmaximal, characteristic
10C24×C4×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2212yes—
12C22×C11×C4⋊C4C2212yes—
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2212yes—
15C22×C11×C4⋊C4C2212yes—
16C22×C11×C4⋊C4C2212yes—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2212yes—
19C22×C11×C22⋊C4C2212yes—
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C11×#398—28no—
23C11×#396—28no—
24C11×#380—28no—
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27C2×C11×#95C2212yes—
28C2×C11×#95C2212yes—
29C2×C11×#95C2212yes—
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2212yes—
32C2×C11×#95C2211yescharacteristic
33C2×C11×#95C2212yes—
34C25×C11C2311yescharacteristic
35C23×C4×C11—24no—
36C23×C4×C11—24no—
37C23×C4×C11—41no—
38C23×C4×C11—41no—
39C23×C4×C11Q814yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2312yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2312yes—
48C2×C11×C4⋊C4—24no—
49C2×C11×C4⋊C4—24no—
50C2×C11×C4⋊C4—24no—
51C2×C11×C4⋊C4—24no—
52C2×C11×C4⋊C4—24no—
53C2×C11×C4⋊C4—24no—
54C2×C11×C4⋊C4—24no—
55C2×C11×C4⋊C4—24no—
56C2×C11×C4⋊C4—24no—
57C2×C11×C4⋊C4—24no—
58C2×C11×C4⋊C4—42no—
59C2×C11×C4⋊C4—42no—
60C2×C11×C4⋊C4—42no—
61C2×C11×C4⋊C4—41no—
62C2×C11×C4⋊C4—42no—
63C2×C11×C4⋊C4—42no—
64C2×C11×C4⋊C4—42no—
65C2×C11×C4⋊C4—42no—
66C2×C11×C4⋊C4—41no—
67C2×C11×C22⋊C4—24no—
68C2×C11×C22⋊C4—24no—
69C2×C11×C22⋊C4—24no—
70C2×C11×C22⋊C4—24no—
71C2×C11×C22⋊C4—41no—
72C2×C11×C22⋊C4—41no—
73C2×C11×C22⋊C4—41no—
74C2×C11×C22⋊C4—41no—
75C2×C11×C22⋊C4—42no—
76C2×C11×C22⋊C4—42no—
77C2×C11×C22⋊C4D414yes—
78C2×C11×C22⋊C4Q814yes—
79C11×#95—24no—
80C11×#95—24no—
81C11×#95—24no—
82C11×#95—24no—
83C11×#95—24no—
84C11×#95—41no—
85C11×#95—41no—
86C11×#95—42no—
87C11×#95D418yes—
88#16305C1111yesmaximal, characteristic, direct product factor, Sylow
89C24×C11—22no—
90C24×C11—22no—
91C24×C11—21no—
92C24×C11—22no—
93C24×C11—21no—
94C24×C11—21no—
95C24×C11—21no—
96C24×C11—22no—
97C24×C11C2×D412yes—
98C24×C11C2×Q812yes—
99C24×C11C2×Q812yes—
100C24×C11C2411yescharacteristic
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—216no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—44no—
147C22×C4×C11—44no—
148C22×C4×C11—48no—
149C22×C4×C11—44no—
150C22×C4×C11C2×D414yes—
151C22×C4×C11C2×D414yes—
152C22×C4×C11C2×D414yes—
153C22×C4×C11C2×D414yes—
154C22×C4×C11C2×Q812yes—
155C22×C4×C11C2×Q812yes—
156C22×C4×C11C2×Q814yes—
157C22×C4×C11#4114yes—
158C11×C4⋊C4—48no—
159C11×C4⋊C4—48no—
160C11×C4⋊C4—48no—
161C11×C4⋊C4—48no—
162C11×C4⋊C4—44no—
163C11×C4⋊C4—48no—
164C11×C4⋊C4—44no—
165C11×C22⋊C4—44no—
166C11×C22⋊C4—44no—
167C11×C22⋊C4—48no—
168C11×C22⋊C4—48no—
169C2×#398C2×C1112yescomplemented
170C2×#396C2×C1112yes—
171C2×#380C2×C1112yes—
172#1444C2×C1112yescomplemented
173#1444C2×C1112yescomplemented
174#1441C2×C1112yescomplemented
175#1439C2×C1111yescharacteristic
176#1439C2×C1111yescharacteristic
177C22⋊#95C2×C1111yescharacteristic
178C23×C11—24no—
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—24no—
186C23×C11—24no—
187C23×C11—24no—
188C23×C11—24no—
189C23×C11—24no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—41no—
195C23×C11—42no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—42no—
199C23×C11—41no—
200C23×C11C4⋊Q814yes—
201C23×C11C22×D412yes—
202C23×C11C22×D411yescharacteristic
203C23×C11C22×Q811yescharacteristic
204C23×C11C22×Q811yescharacteristic
205C23×C11C2×#4112yes—
206C23×C11H(5,𝔽2)11yescharacteristic
207C23×C11H(5,𝔽2)11yescharacteristic
208C23×C11H(5,𝔽2)12yes—
209C23×C11H(5,𝔽2)11yescharacteristic
210C23×C112−1+411yescharacteristic
211C23×C112−1+412yes—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—416no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—41no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—41no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11C22⋊Q818yes—
265C24×C4C22×C1111yescharacteristic
266C22×C4⋊C4C22×C1112yes—
267C22×C4⋊C4C22×C1112yes—
268C22×C4⋊C4C22×C1111yescharacteristic
269C22×C4⋊C4C22×C1112yes—
270C22×C4⋊C4C22×C1112yes—
271C22×C4⋊C4C22×C1112yes—
272C22×C4⋊C4C22×C1111yescharacteristic
273C22×C22⋊C4C22×C1112yes—
274C22×C22⋊C4C22×C1112yes—
275C22×C22⋊C4C22×C1111yescharacteristic
276C22×C22⋊C4C22×C1111yescharacteristic
277#398—28no—
278#396—28no—
279#380—28no—
280C2×#95C22×C1112yes—
281C2×#95C22×C1112yes—
282C2×#95C22×C1112yes—
283C2×#95C22×C1112yes—
284C2×#95C22×C1112yes—
285C2×#95C22×C1111yescharacteristic
286C2×#95C22×C1112yes—
287C2×#95C22×C1111yescharacteristic
288C2×#95C22×C1112yes—
289C22×C11—24no—
290C22×C11—28no—
291C22×C11—42no—
292C22×C11—44no—
293C22×C11—44no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—44no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11C2×C22⋊Q812yes—
301C22×C11C2×C4⋊Q811yescharacteristic
302C22×C11#53411yescharacteristic
303C22×C11#53712yes—
304C22×C11#53712yes—
305C22×C11#53711yescharacteristic
306C22×C11#54012yes—
307C22×C11#54112yes—
308C22×C11#54311yescharacteristic
309C22×C11#54311yescharacteristic
310C22×C11#54412yes—
311C22×C11#54411yescharacteristic
312C22×C11#54411yescharacteristic
313C22×C11D4212yes—
314C22×C11D4211yescharacteristic
315C22×C11#54612yes—
316C22×C11#54712yes—
317C22×C11D4×Q812yes—
318C22×C11#55111yescharacteristic
319C22×C11#55412yes—
320C22×C11#56011yescharacteristic
321C22×C11#56212yes—
322C22×C11#56311yescharacteristic
323C4×C11—28no—
324C4×C11—44no—
325C4×C11—44no—
326C4×C11—44no—
327C4×C11—42no—
328C4×C11—42no—
329C4×C11—82no—
330C4×C11—82no—
331C25C23×C1111yescharacteristic
332C23×C4—24no—
333C23×C4—24no—
334C23×C4—41no—
335C23×C4—41no—
336C23×C4Q8×C1114yes—
337C23×C4C23×C1112yes—
338C23×C4C23×C1112yes—
339C23×C4C23×C1112yes—
340C23×C4C23×C1112yes—
341C23×C4C23×C1112yes—
342C23×C4C23×C1111yescharacteristic
343C23×C4C23×C1111yescharacteristic
344C23×C4C23×C1112yes—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—41no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4—41no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—41no—
369C2×C22⋊C4—41no—
370C2×C22⋊C4—41no—
371C2×C22⋊C4—41no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4D4×C1114yes—
375C2×C22⋊C4Q8×C1114yes—
376#95—24no—
377#95—24no—
378#95—24no—
379#95—24no—
380#95—24no—
381#95—41no—
382#95—41no—
383#95—42no—
384#95D4×C1118yes—
385C2×C11—44no—
386C2×C11#243711yescharacteristic
387C2×C11#244012yes—
388C2×C11#262912yes—
389C2×C11#265911yescharacteristic
390C2×C11#267112yes—
391C2×C11#267511yescharacteristic
392C2×C11#268311yescharacteristic
393C2×C11#270412yes—
394C2×C11#272211yescharacteristic
395C2×C11#274811yescharacteristic
396C2×C11#284111yescharacteristic
397C24—22no—
398C24—22no—
399C24—21no—
400C24—22no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—22no—
405C24C2×D4×C1112yes—
406C24C2×Q8×C1112yes—
407C24C2×Q8×C1112yes—
408C24C24×C1111yescharacteristic
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—216no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—44no—
455C22×C4—44no—
456C22×C4—48no—
457C22×C4—44no—
458C22×C4C2×D4×C1114yes—
459C22×C4C2×D4×C1114yes—
460C22×C4C2×D4×C1114yes—
461C22×C4C2×D4×C1114yes—
462C22×C4C2×Q8×C1112yes—
463C22×C4C2×Q8×C1112yes—
464C22×C4C2×Q8×C1114yes—
465C22×C4C11×#4114yes—
466C4⋊C4—48no—
467C4⋊C4—48no—
468C4⋊C4—48no—
469C4⋊C4—48no—
470C4⋊C4—44no—
471C4⋊C4—48no—
472C4⋊C4—44no—
473C22⋊C4—44no—
474C22⋊C4—44no—
475C22⋊C4—48no—
476C22⋊C4—48no—
477C11#1630511yescharacteristic, direct product factor, Sylow
478C23—24no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—22no—
484C23—22no—
485C23—24no—
486C23—24no—
487C23—24no—
488C23—24no—
489C23—24no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—41no—
495C23—42no—
496C23—41no—
497C23—41no—
498C23—42no—
499C23—41no—
500C23C11×C4⋊Q814yes—
501C23C22×D4×C1112yes—
502C23C22×D4×C1111yescharacteristic
503C23C22×Q8×C1111yescharacteristic
504C23C22×Q8×C1111yescharacteristic
505C23C2×C11×#4112yes—
506C23C11×H(5,𝔽2)11yescharacteristic
507C23C11×H(5,𝔽2)11yescharacteristic
508C23C11×H(5,𝔽2)12yes—
509C23C11×H(5,𝔽2)11yescharacteristic
510C23C11×2−1+411yescharacteristic
511C23C11×2−1+412yes—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—416no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4C11×C22⋊Q818yes—
565C22—24no—
566C22—28no—
567C22—44no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—44no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—44no—
576C22C2×C11×C22⋊Q812yes—
577C22C2×C11×C4⋊Q811yescharacteristic
578C22C11×#53411yescharacteristic
579C22C11×#53711yescharacteristic
580C22C11×#53712yes—
581C22C11×#53712yes—
582C22C11×#54012yes—
583C22C11×#54112yes—
584C22C11×#54311yescharacteristic
585C22C11×#54311yescharacteristic
586C22C11×#54411yescharacteristic
587C22C11×#54411yescharacteristic
588C22C11×#54412yes—
589C22D42×C1112yes—
590C22D42×C1111yescharacteristic
591C22C11×#54612yes—
592C22C11×#54712yes—
593C22D4×Q8×C1112yes—
594C22C11×#55111yescharacteristic
595C22C11×#55412yes—
596C22C11×#56011yescharacteristic
597C22C11×#56212yes—
598C22C11×#56311yescharacteristic
599C4—28no—
600C4—44no—
601C4—44no—
602C4—44no—
603C4—42no—
604C4—42no—
605C4—82no—
606C4—82no—
607C2—44no—
608C2C11×#243711yescharacteristic
609C2C11×#244012yes—
610C2C11×#262912yes—
611C2C11×#265911yescharacteristic
612C2C11×#267112yes—
613C2C11×#267511yescharacteristic
614C2C11×#268311yescharacteristic
615C2C11×#270412yes—
616C2C11×#272211yescharacteristic
617C2C11×#274811yescharacteristic
618C2C11×#284111yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC24C24×C11
prime radicalC25×C11C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#398C2semidirect
4. C11×#1444C2semidirect
5. C11×#1444C2semidirect
6. C11×#1441C2semidirect
88. #16305C11direct (N × H)
169. C2×#398C2×C11semidirect
172. #1444C2×C11semidirect
173. #1444C2×C11semidirect
174. #1441C2×C11semidirect
477. C11#16305direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3982
C2×C11×#3962
C2×C11×#3802
C11×#14442
C11×#14412
C11×#14392
C11×C22⋊#952
#1630511