Finite Group Databasebeta

← C11×#15506 #14592699

Subgroups — C11×#15506 #14592699

Order 2816.

1954 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#393C212yesmaximal, complemented
2C2×C11×#386C212yesmaximal
3C11×#1446C211yesmaximal, characteristic, complemented
4C11×#1445C211yesmaximal, characteristic, complemented
5C11×#1443C212yesmaximal, complemented
6C11×#1439C212yesmaximal, complemented
7C11×#1438C211yesmaximal, characteristic
8C11×C22⋊#95C212yesmaximal, complemented
9C11×C22⋊#95C212yesmaximal, complemented
10C23×Q8×C11C2211yescharacteristic
11C23×D4×C11C2211yescharacteristic
12C24×C4×C11C2212yes—
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2212yes—
15C22×C11×C22⋊C4C2212yes—
16C22×C11×C22⋊C4C2212yes—
17C22×C11×C22⋊C4C2212yes—
18C22×C11×C22⋊C4C2212yes—
19C11×#393—28no—
20C11×#386—28no—
21C2×C11×#95C2212yes—
22C2×C11×#95C2212yes—
23C2×C11×#95C2212yes—
24C2×C11×#95C2212yes—
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27C2×C11×#95C2212yes—
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2212yes—
31C2×C11×#95C2211yescharacteristic
32C2×C11×#95C2211yescharacteristic
33C25×C11C2312yes—
34C22×Q8×C11—24no—
35C22×Q8×C11—22no—
36C22×Q8×C11—41no—
37C22×Q8×C11—42no—
38C22×Q8×C11—41no—
39C22×D4×C11—24no—
40C22×D4×C11—24no—
41C22×D4×C11—41no—
42C22×D4×C11—41no—
43C22×D4×C11Q814yescomplemented
44C23×C4×C11—24no—
45C23×C4×C11—24no—
46C23×C4×C11—24no—
47C23×C4×C11—42no—
48C23×C4×C11—42no—
49C23×C4×C11—42no—
50C23×C4×C11—42no—
51C23×C4×C11C2312yes—
52C23×C4×C11C2312yes—
53C23×C4×C11C2312yes—
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2312yes—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—41no—
61C2×C11×C4⋊C4—41no—
62C2×C11×C22⋊C4—24no—
63C2×C11×C22⋊C4—24no—
64C2×C11×C22⋊C4—24no—
65C2×C11×C22⋊C4—24no—
66C2×C11×C22⋊C4—24no—
67C2×C11×C22⋊C4—24no—
68C2×C11×C22⋊C4—24no—
69C2×C11×C22⋊C4—24no—
70C2×C11×C22⋊C4—42no—
71C2×C11×C22⋊C4—42no—
72C2×C11×C22⋊C4—42no—
73C2×C11×C22⋊C4—42no—
74C2×C11×C22⋊C4—42no—
75C2×C11×C22⋊C4—42no—
76C2×C11×C22⋊C4D418yes—
77C11×#95—24no—
78C11×#95—24no—
79C11×#95—24no—
80C11×#95—24no—
81C11×#95—24no—
82C11×#95—24no—
83C11×#95—42no—
84C11×#95—41no—
85C11×#95—41no—
86C11×#95—41no—
87C11×#95—42no—
88C11×#95—41no—
89#15506C1111yesmaximal, characteristic, direct product factor, Sylow
90C24×C11—22no—
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—22no—
95C24×C11—22no—
96C24×C11—22no—
97C24×C11—22no—
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—22no—
101C24×C11—22no—
102C24×C11C2×D414yes—
103C24×C11C2×Q814yes—
104C24×C11#4114yes—
105C24×C11C2411yescharacteristic
106C2×Q8×C11—44no—
107C2×Q8×C11—48no—
108C2×Q8×C11—48no—
109C2×Q8×C11—44no—
110C2×Q8×C11—44no—
111C2×D4×C11—216no—
112C2×D4×C11—44no—
113C2×D4×C11—44no—
114C2×D4×C11—48no—
115C2×D4×C11—44no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
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—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—48no—
161C22×C4×C11—48no—
162C22×C4×C11—48no—
163C22×C4×C11—48no—
164C22×C4×C11—48no—
165C22×C4×C11—48no—
166C22×C4×C11—48no—
167C22×C4×C11C2×D414yes—
168C22×C4×C11C2×D414yes—
169C22×C4×C11C2×Q812yes—
170C22×C4×C11#4114yes—
171C22×C4×C11#4112yes—
172C22×C4×C11#4112yes—
173C11×C4⋊C4—44no—
174C11×C22⋊C4—48no—
175C11×C22⋊C4—48no—
176C11×C22⋊C4—48no—
177C11×C22⋊C4—48no—
178C11×C22⋊C4—48no—
179C2×#393C2×C1112yescomplemented
180C2×#386C2×C1112yes—
181#1446C2×C1111yescharacteristic, complemented
182#1445C2×C1111yescharacteristic, complemented
183#1443C2×C1112yescomplemented
184#1439C2×C1112yescomplemented
185#1438C2×C1111yescharacteristic
186C22⋊#95C2×C1112yescomplemented
187C22⋊#95C2×C1112yescomplemented
188C23×C11—24no—
189C23×C11—24no—
190C23×C11—24no—
191C23×C11—24no—
192C23×C11—24no—
193C23×C11—24no—
194C23×C11—24no—
195C23×C11—24no—
196C23×C11—24no—
197C23×C11—24no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11—24no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11C22⋊Q818yes—
223C23×C11C22×D412yes—
224C23×C11C22×Q811yescharacteristic
225C23×C11C2×#4112yes—
226C23×C11C2×#4111yescharacteristic
227C23×C11C2×#4112yes—
228C23×C11C2×#4111yescharacteristic
229C23×C11H(5,𝔽2)11yescharacteristic
230C23×C11H(5,𝔽2)12yes—
231C23×C11H(5,𝔽2)11yescharacteristic
232C23×C11H(5,𝔽2)11yescharacteristic
233C23×C11H(5,𝔽2)11yescharacteristic
234Q8×C11—416no—
235D4×C11—416no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—22no—
240C2×C4×C11—24no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—432no—
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—41no—
261C2×C4×C11—41no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—41no—
266C2×C4×C11—42no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—42no—
270C2×C4×C11—41no—
271C2×C4×C11—42no—
272C2×C4×C11—42no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11—42no—
278C2×C4×C11—42no—
279C2×C4×C11—42no—
280C2×C4×C11—42no—
281C2×C4×C11—42no—
282C2×C4×C11—42no—
283C2×C4×C11—42no—
284C2×C4×C11—42no—
285C2×C4×C11—42no—
286C2×C4×C11—42no—
287C23×Q8C22×C1111yescharacteristic
288C23×D4C22×C1111yescharacteristic
289C24×C4C22×C1112yes—
290C22×C4⋊C4C22×C1111yescharacteristic
291C22×C22⋊C4C22×C1112yes—
292C22×C22⋊C4C22×C1112yes—
293C22×C22⋊C4C22×C1112yes—
294C22×C22⋊C4C22×C1112yes—
295C22×C22⋊C4C22×C1112yes—
296#393—28no—
297#386—28no—
298C2×#95C22×C1112yes—
299C2×#95C22×C1112yes—
300C2×#95C22×C1112yes—
301C2×#95C22×C1112yes—
302C2×#95C22×C1112yes—
303C2×#95C22×C1112yes—
304C2×#95C22×C1112yes—
305C2×#95C22×C1111yescharacteristic
306C2×#95C22×C1111yescharacteristic
307C2×#95C22×C1112yes—
308C2×#95C22×C1111yescharacteristic
309C2×#95C22×C1111yescharacteristic
310C22×C11—28no—
311C22×C11—28no—
312C22×C11—28no—
313C22×C11—44no—
314C22×C11—44no—
315C22×C11—44no—
316C22×C11—44no—
317C22×C11—44no—
318C22×C11—44no—
319C22×C11—44no—
320C22×C11—44no—
321C22×C11—44no—
322C22×C11—44no—
323C22×C11—44no—
324C22×C11—44no—
325C22×C11C2×C22⋊Q812yes—
326C22×C11#52912yes—
327C22×C11#53212yes—
328C22×C11#53412yes—
329C22×C11#53811yescharacteristic
330C22×C11#53812yes—
331C22×C11#53812yes—
332C22×C11#53811yescharacteristic
333C22×C11#54311yescharacteristic
334C22×C11D4211yescharacteristic
335C22×C11#54612yes—
336C22×C11#54612yes—
337C22×C11#54612yes—
338C22×C11#55112yes—
339C22×C11#55112yes—
340C22×C11#55111yescharacteristic
341C22×C11#55411yescharacteristic
342C22×C11#55412yes—
343C22×C11#55411yescharacteristic
344C22×C11#55511yescharacteristic
345C22×C11#55911yescharacteristic
346C22×C11#56011yescharacteristic
347C22×C11H(3,𝔽4)11yescharacteristic
348C4×C11—44no—
349C4×C11—42no—
350C4×C11—44no—
351C4×C11—44no—
352C4×C11—42no—
353C4×C11—42no—
354C4×C11—82no—
355C4×C11—82no—
356C25C23×C1112yes—
357C22×Q8—24no—
358C22×Q8—22no—
359C22×Q8—41no—
360C22×Q8—42no—
361C22×Q8—41no—
362C22×D4—24no—
363C22×D4—24no—
364C22×D4—41no—
365C22×D4—41no—
366C22×D4Q8×C1114yescomplemented
367C23×C4—24no—
368C23×C4—24no—
369C23×C4—24no—
370C23×C4—42no—
371C23×C4—42no—
372C23×C4—42no—
373C23×C4—42no—
374C23×C4C23×C1112yes—
375C23×C4C23×C1112yes—
376C23×C4C23×C1112yes—
377C23×C4C23×C1112yes—
378C23×C4C23×C1111yescharacteristic
379C23×C4C23×C1111yescharacteristic
380C23×C4C23×C1111yescharacteristic
381C23×C4C23×C1112yes—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—41no—
384C2×C4⋊C4—41no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4D4×C1118yes—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—42no—
407#95—41no—
408#95—41no—
409#95—41no—
410#95—42no—
411#95—41no—
412C2×C11—48no—
413C2×C11#243711yescharacteristic
414C2×C11#245012yes—
415C2×C11#255511yescharacteristic
416C2×C11#255712yes—
417C2×C11#256412yes—
418C2×C11#257211yescharacteristic
419C2×C11#266811yescharacteristic
420C2×C11#268412yes—
421C2×C11#276011yescharacteristic
422C2×C11#278411yescharacteristic
423C2×C11#280411yescharacteristic
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24C2×D4×C1114yes—
437C24C2×Q8×C1114yes—
438C24C11×#4114yes—
439C24C24×C1111yescharacteristic
440C2×Q8—44no—
441C2×Q8—48no—
442C2×Q8—48no—
443C2×Q8—44no—
444C2×Q8—44no—
445C2×D4—216no—
446C2×D4—44no—
447C2×D4—44no—
448C2×D4—48no—
449C2×D4—44no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—48no—
495C22×C4—48no—
496C22×C4—48no—
497C22×C4—48no—
498C22×C4—48no—
499C22×C4—48no—
500C22×C4—48no—
501C22×C4C2×D4×C1114yes—
502C22×C4C2×D4×C1114yes—
503C22×C4C2×Q8×C1112yes—
504C22×C4C11×#4114yes—
505C22×C4C11×#4112yes—
506C22×C4C11×#4112yes—
507C4⋊C4—44no—
508C22⋊C4—48no—
509C22⋊C4—48no—
510C22⋊C4—48no—
511C22⋊C4—48no—
512C22⋊C4—48no—
513C11#1550611yescharacteristic, direct product factor, Sylow
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—24no—
521C23—24no—
522C23—24no—
523C23—24no—
524C23—24no—
525C23—24no—
526C23—24no—
527C23—24no—
528C23—24no—
529C23—24no—
530C23—24no—
531C23—24no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23C11×C22⋊Q818yes—
549C23C22×D4×C1112yes—
550C23C22×Q8×C1111yescharacteristic
551C23C2×C11×#4112yes—
552C23C2×C11×#4111yescharacteristic
553C23C2×C11×#4112yes—
554C23C2×C11×#4111yescharacteristic
555C23C11×H(5,𝔽2)11yescharacteristic
556C23C11×H(5,𝔽2)12yes—
557C23C11×H(5,𝔽2)11yescharacteristic
558C23C11×H(5,𝔽2)11yescharacteristic
559C23C11×H(5,𝔽2)11yescharacteristic
560Q8—416no—
561D4—416no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—432no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—42no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C22—28no—
614C22—28no—
615C22—28no—
616C22—44no—
617C22—44no—
618C22—44no—
619C22—44no—
620C22—44no—
621C22—44no—
622C22—44no—
623C22—44no—
624C22—44no—
625C22—44no—
626C22—44no—
627C22—44no—
628C22C2×C11×C22⋊Q812yes—
629C22C11×#52912yes—
630C22C11×#53212yes—
631C22C11×#53412yes—
632C22C11×#53811yescharacteristic
633C22C11×#53812yes—
634C22C11×#53812yes—
635C22C11×#53811yescharacteristic
636C22C11×#54311yescharacteristic
637C22D42×C1111yescharacteristic
638C22C11×#54612yes—
639C22C11×#54612yes—
640C22C11×#54612yes—
641C22C11×#55112yes—
642C22C11×#55111yescharacteristic
643C22C11×#55112yes—
644C22C11×#55411yescharacteristic
645C22C11×#55412yes—
646C22C11×#55411yescharacteristic
647C22C11×#55511yescharacteristic
648C22C11×#55911yescharacteristic
649C22C11×#56011yescharacteristic
650C22C11×H(3,𝔽4)11yescharacteristic
651C4—44no—
652C4—42no—
653C4—44no—
654C4—44no—
655C4—42no—
656C4—42no—
657C4—82no—
658C4—82no—
659C2—48no—
660C2C11×#243711yescharacteristic
661C2C11×#245012yes—
662C2C11×#255511yescharacteristic
663C2C11×#255712yes—
664C2C11×#256412yes—
665C2C11×#257211yescharacteristic
666C2C11×#266811yescharacteristic
667C2C11×#268412yes—
668C2C11×#276011yescharacteristic
669C2C11×#278411yescharacteristic
670C2C11×#280411yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC24C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#393C2semidirect
3. C11×#1446C2semidirect
4. C11×#1445C2semidirect
5. C11×#1443C2semidirect
6. C11×#1439C2semidirect
8. C11×C22⋊#95C2semidirect
9. C11×C22⋊#95C2semidirect
43. C22×D4×C11Q8semidirect
89. #15506C11direct (N × H)
179. C2×#393C2×C11semidirect
181. #1446C2×C11semidirect
182. #1445C2×C11semidirect
183. #1443C2×C11semidirect
184. #1439C2×C11semidirect
186. C22⋊#95C2×C11semidirect
187. C22⋊#95C2×C11semidirect
366. C22×D4Q8×C11semidirect
513. C11#15506direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3932
C2×C11×#3862
C11×#14462
C11×#14452
C11×#14432
C11×#14392
C11×#14382
C11×C22⋊#952
#1550611