Finite Group Databasebeta

← C11×#14516 #14591709

Subgroups — C11×#14516 #14591709

Order 2816.

1666 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#386C211yesmaximal, characteristic
2C11×#1443C212yesmaximal, complemented
3C11×#1440C212yesmaximal, complemented
4C11×#1438C211yesmaximal, characteristic
5C11×#1438C211yesmaximal, characteristic
6C11×#1437C212yesmaximal, complemented
7C11×#1437C212yesmaximal, complemented
8C11×#1434C212yesmaximal, complemented
9C11×C22⋊#95C212yesmaximal, complemented
10C23×D4×C11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C22×C11×C22⋊C4C2212yes—
13C22×C11×C22⋊C4C2212yes—
14C22×C11×C22⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2212yes—
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2212yes—
19C22×C42×C11C2212yes—
20C11×#386C418yescomplemented
21C2×C11×#95C2212yes—
22C2×C11×#95C2212yes—
23C2×C11×#95C2212yes—
24C2×C11×#95C2212yes—
25C2×C11×#95C2212yes—
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2212yes—
28C2×C11×#95C2212yes—
29C2×C11×#95C2212yes—
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2212yes—
32C25×C11C2311yescharacteristic
33C25×C11C2311yescharacteristic
34C22×D4×C11—24no—
35C22×D4×C11—42no—
36C22×D4×C11—41no—
37C22×D4×C11—41no—
38C22×D4×C11C2×C414yes—
39C23×C4×C11—41no—
40C23×C4×C11—41no—
41C23×C4×C11—42no—
42C23×C4×C11—42no—
43C23×C4×C11C2×C414yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2312yes—
46C23×C4×C11C2312yes—
47C23×C4×C11C2312yes—
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2312yes—
50C23×C4×C11C2312yes—
51C2×C11×C22⋊C4—24no—
52C2×C11×C22⋊C4—24no—
53C2×C11×C22⋊C4—24no—
54C2×C11×C22⋊C4—24no—
55C2×C11×C22⋊C4—24no—
56C2×C11×C22⋊C4—24no—
57C2×C11×C22⋊C4—42no—
58C2×C11×C22⋊C4—42no—
59C2×C11×C22⋊C4—42no—
60C2×C11×C22⋊C4—41no—
61C2×C11×C22⋊C4—42no—
62C2×C11×C22⋊C4—42no—
63C2×C11×C22⋊C4—42no—
64C2×C11×C22⋊C4—42no—
65C2×C11×C22⋊C4—41no—
66C2×C11×C22⋊C4—42no—
67C2×C11×C22⋊C4C2×C414yes—
68C2×C11×C22⋊C4C2×C418yes—
69C2×C42×C11—24no—
70C2×C42×C11—42no—
71C2×C42×C11—42no—
72C11×#95—24no—
73C11×#95—41no—
74C11×#95—42no—
75C11×#95—42no—
76C11×#95—42no—
77C11×#95—42no—
78C11×#95—42no—
79C11×#95—42no—
80C11×#95—42no—
81C11×#95—41no—
82C11×#95C2×C418yes—
83#14516C1111yesmaximal, characteristic, direct product factor, Sylow
84C24×C11—22no—
85C24×C11—22no—
86C24×C11—22no—
87C24×C11—22no—
88C24×C11—22no—
89C24×C11—21no—
90C24×C11—21no—
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—22no—
95C24×C11—22no—
96C24×C11—22no—
97C24×C11—21no—
98C24×C11—21no—
99C24×C11C22×C412yes—
100C24×C11C22×C412yes—
101C24×C11#4114yes—
102C24×C11C2411yescharacteristic
103C2×D4×C11—28no—
104C2×D4×C11—44no—
105C2×D4×C11—44no—
106C2×D4×C11—48no—
107C2×D4×C11—48no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
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—22no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
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—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—48no—
151C22×C4×C11—44no—
152C22×C4×C11—48no—
153C22×C4×C11—44no—
154C22×C4×C11—44no—
155C22×C4×C11C22×C412yes—
156C22×C4×C11C22×C414yes—
157C22×C4×C11C22×C414yes—
158C22×C4×C11#4114yes—
159C22×C4×C11#4114yes—
160C11×C22⋊C4—48no—
161C11×C22⋊C4—44no—
162C11×C22⋊C4—44no—
163C11×C22⋊C4—48no—
164C11×C22⋊C4—48no—
165C11×C22⋊C4—48no—
166C11×C22⋊C4—44no—
167C42×C11—48no—
168C2×#386C2×C1111yescharacteristic
169#1443C2×C1112yescomplemented
170#1440C2×C1112yescomplemented
171#1438C2×C1111yescharacteristic
172#1438C2×C1111yescharacteristic
173#1437C2×C1112yescomplemented
174#1437C2×C1112yescomplemented
175#1434C2×C1112yescomplemented
176C22⋊#95C2×C1112yescomplemented
177C23×C11—24no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—24no—
181C23×C11—24no—
182C23×C11—24no—
183C23×C11—24no—
184C23×C11—24no—
185C23×C11—24no—
186C23×C11—24no—
187C23×C11—22no—
188C23×C11—24no—
189C23×C11—24no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—41no—
197C23×C11—42no—
198C23×C11—41no—
199C23×C11—42no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—41no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—41no—
215C23×C11—42no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11#11714yes—
219C23×C11C23×C411yescharacteristic
220C23×C11C2×#4112yes—
221C23×C11C2×#4112yes—
222C23×C11C2×#4112yes—
223C23×C11H(5,𝔽2)12yes—
224C23×C11H(5,𝔽2)12yes—
225C23×C11H(5,𝔽2)11yescharacteristic
226C23×C11H(5,𝔽2)11yescharacteristic
227C23×C11H(5,𝔽2)12yes—
228D4×C11—416no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—416no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
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×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—42no—
269C2×C4×C11—42no—
270C2×C4×C11—42no—
271C2×C4×C11—42no—
272C2×C4×C11—42no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C23×D4C22×C1111yescharacteristic
278C24×C4C22×C1111yescharacteristic
279C22×C22⋊C4C22×C1112yes—
280C22×C22⋊C4C22×C1112yes—
281C22×C22⋊C4C22×C1111yescharacteristic
282C22×C22⋊C4C22×C1112yes—
283C22×C22⋊C4C22×C1111yescharacteristic
284C22×C22⋊C4C22×C1111yescharacteristic
285C22×C22⋊C4C22×C1112yes—
286C22×C42C22×C1112yes—
287#386C4×C1118yescomplemented
288C2×#95C22×C1112yes—
289C2×#95C22×C1112yes—
290C2×#95C22×C1112yes—
291C2×#95C22×C1112yes—
292C2×#95C22×C1112yes—
293C2×#95C22×C1111yescharacteristic
294C2×#95C22×C1112yes—
295C2×#95C22×C1112yes—
296C2×#95C22×C1112yes—
297C2×#95C22×C1111yescharacteristic
298C2×#95C22×C1112yes—
299C22×C11—24no—
300C22×C11—28no—
301C22×C11—44no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—44no—
305C22×C11—44no—
306C22×C11—44no—
307C22×C11—44no—
308C22×C11—42no—
309C22×C11—44no—
310C22×C11—44no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11—82no—
314C22×C11—82no—
315C22×C11—82no—
316C22×C11—82no—
317C22×C11C2×#11711yescharacteristic
318C22×C11C4×#4112yes—
319C22×C11#51811yescharacteristic
320C22×C11#51811yescharacteristic
321C22×C11#51812yes—
322C22×C11#53812yes—
323C22×C11#53812yes—
324C22×C11#53812yes—
325C22×C11#53812yes—
326C22×C11#54012yes—
327C22×C11#54012yes—
328C22×C11#55112yes—
329C22×C11#55112yes—
330C22×C11#55111yescharacteristic
331C22×C11#55312yes—
332C22×C11#55312yes—
333C22×C11#55312yes—
334C22×C11#55911yescharacteristic
335C22×C11#56012yes—
336C22×C11#56011yescharacteristic
337C22×C11H(3,𝔽4)11yescharacteristic
338C4×C11—42no—
339C4×C11—44no—
340C4×C11—44no—
341C4×C11—44no—
342C4×C11—44no—
343C4×C11—82no—
344C4×C11—82no—
345C25C23×C1111yescharacteristic
346C25C23×C1111yescharacteristic
347C22×D4—24no—
348C22×D4—42no—
349C22×D4—41no—
350C22×D4—41no—
351C22×D4C2×C4×C1114yes—
352C23×C4—41no—
353C23×C4—41no—
354C23×C4—42no—
355C23×C4—42no—
356C23×C4C2×C4×C1114yes—
357C23×C4C23×C1112yes—
358C23×C4C23×C1112yes—
359C23×C4C23×C1112yes—
360C23×C4C23×C1112yes—
361C23×C4C23×C1111yescharacteristic
362C23×C4C23×C1112yes—
363C23×C4C23×C1112yes—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—41no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—41no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4C2×C4×C1114yes—
381C2×C22⋊C4C2×C4×C1118yes—
382C2×C42—24no—
383C2×C42—42no—
384C2×C42—42no—
385#95—24no—
386#95—41no—
387#95—42no—
388#95—42no—
389#95—42no—
390#95—42no—
391#95—42no—
392#95—42no—
393#95—42no—
394#95—41no—
395#95C2×C4×C1118yes—
396C2×C11—44no—
397C2×C11—82no—
398C2×C11#231211yescharacteristic
399C2×C11#233312yes—
400C2×C11#235312yes—
401C2×C11#237411yescharacteristic
402C2×C11#237511yescharacteristic
403C2×C11#274912yes—
404C2×C11#275312yes—
405C2×C11#277812yes—
406C2×C11#279712yes—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—21no—
413C24—21no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—21no—
421C24—21no—
422C24C22×C4×C1112yes—
423C24C22×C4×C1112yes—
424C24C11×#4114yes—
425C24C24×C1111yescharacteristic
426C2×D4—28no—
427C2×D4—44no—
428C2×D4—44no—
429C2×D4—48no—
430C2×D4—48no—
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—22no—
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—21no—
452C22×C4—21no—
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—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—48no—
474C22×C4—44no—
475C22×C4—48no—
476C22×C4—44no—
477C22×C4—44no—
478C22×C4C22×C4×C1112yes—
479C22×C4C22×C4×C1114yes—
480C22×C4C22×C4×C1114yes—
481C22×C4C11×#4114yes—
482C22×C4C11×#4114yes—
483C22⋊C4—48no—
484C22⋊C4—44no—
485C22⋊C4—44no—
486C22⋊C4—48no—
487C22⋊C4—48no—
488C22⋊C4—48no—
489C22⋊C4—44no—
490C42—48no—
491C11#1451611yescharacteristic, direct product factor, Sylow
492C23—24no—
493C23—22no—
494C23—22no—
495C23—24no—
496C23—24no—
497C23—24no—
498C23—24no—
499C23—24no—
500C23—24no—
501C23—24no—
502C23—22no—
503C23—24no—
504C23—24no—
505C23—22no—
506C23—22no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—41no—
512C23—42no—
513C23—41no—
514C23—42no—
515C23—41no—
516C23—41no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—41no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—41no—
530C23—42no—
531C23—41no—
532C23—41no—
533C23C11×#11714yes—
534C23C23×C4×C1111yescharacteristic
535C23C2×C11×#4112yes—
536C23C2×C11×#4112yes—
537C23C2×C11×#4112yes—
538C23C11×H(5,𝔽2)12yes—
539C23C11×H(5,𝔽2)12yes—
540C23C11×H(5,𝔽2)11yescharacteristic
541C23C11×H(5,𝔽2)11yescharacteristic
542C23C11×H(5,𝔽2)12yes—
543D4—416no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—416no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
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—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C22—24no—
593C22—28no—
594C22—44no—
595C22—44no—
596C22—44no—
597C22—44no—
598C22—44no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—44no—
603C22—44no—
604C22—42no—
605C22—42no—
606C22—82no—
607C22—82no—
608C22—82no—
609C22—82no—
610C22C2×C11×#11711yescharacteristic
611C22C4×C11×#4112yes—
612C22C11×#51811yescharacteristic
613C22C11×#51811yescharacteristic
614C22C11×#51812yes—
615C22C11×#53812yes—
616C22C11×#53812yes—
617C22C11×#53812yes—
618C22C11×#53812yes—
619C22C11×#54012yes—
620C22C11×#54012yes—
621C22C11×#55111yescharacteristic
622C22C11×#55112yes—
623C22C11×#55112yes—
624C22C11×#55312yes—
625C22C11×#55312yes—
626C22C11×#55312yes—
627C22C11×#55911yescharacteristic
628C22C11×#56012yes—
629C22C11×#56011yescharacteristic
630C22C11×H(3,𝔽4)11yescharacteristic
631C4—44no—
632C4—44no—
633C4—42no—
634C4—44no—
635C4—44no—
636C4—82no—
637C4—82no—
638C2—44no—
639C2—82no—
640C2C11×#231211yescharacteristic
641C2C11×#233312yes—
642C2C11×#235312yes—
643C2C11×#237411yescharacteristic
644C2C11×#237511yescharacteristic
645C2C11×#274912yes—
646C2C11×#275312yes—
647C2C11×#277812yes—
648C2C11×#279712yes—
subgroupG/H
center, socleC24×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1443C2semidirect
3. C11×#1440C2semidirect
6. C11×#1437C2semidirect
7. C11×#1437C2semidirect
8. C11×#1434C2semidirect
9. C11×C22⋊#95C2semidirect
20. C11×#386C4semidirect
83. #14516C11direct (N × H)
169. #1443C2×C11semidirect
170. #1440C2×C11semidirect
173. #1437C2×C11semidirect
174. #1437C2×C11semidirect
175. #1434C2×C11semidirect
176. C22⋊#95C2×C11semidirect
287. #386C4×C11semidirect
491. C11#14516direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3862
C11×#14432
C11×#14402
C11×#14382
C11×#14372
C11×#14342
C11×C22⋊#952
#1451611