Finite Group Databasebeta

← C11×#14506 #14591699

Subgroups — C11×#14506 #14591699

Order 2816.

1962 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#123C211yesmaximal, characteristic
2C2×C11×#388C212yesmaximal, complemented
3C11×#1445C212yesmaximal, complemented
4C11×#1439C212yesmaximal, complemented
5C11×#1438C211yesmaximal, characteristic
6C11×#1438C211yesmaximal, characteristic
7C11×#1437C212yesmaximal, complemented
8C11×C4⋊#95C212yesmaximal, complemented
9C11×C22⋊#95C212yesmaximal, complemented
10C23×D4×C11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C2×C11×#123—28no—
13C2×C11×#123C418yescomplemented
14C22×C11×C4⋊C4C2212yes—
15C22×C11×C4⋊C4C2212yes—
16C22×C11×C22⋊C4C2212yes—
17C22×C11×C22⋊C4C2212yes—
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C11×C22⋊C4C2212yes—
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C42×C11C2212yes—
24C11×#388—28no—
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27C2×C11×#95C2212yes—
28C2×C11×#95C2212yes—
29C2×C11×#95C2212yes—
30C2×C11×#95C2212yes—
31C2×C11×#95C2211yescharacteristic
32C2×C11×#95C2212yes—
33C2×C11×#95C2211yescharacteristic
34C25×C11C2311yescharacteristic
35C25×C11C2311yescharacteristic
36C22×D4×C11—24no—
37C22×D4×C11—42no—
38C22×D4×C11—41no—
39C22×D4×C11—41no—
40C22×D4×C11C2×C414yes—
41C23×C4×C11—24no—
42C23×C4×C11—42no—
43C23×C4×C11—41no—
44C23×C4×C11—41no—
45C23×C4×C11C2×C414yes—
46C23×C4×C11C2312yes—
47C23×C4×C11C2312yes—
48C23×C4×C11C2312yes—
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2312yes—
51C23×C4×C11C2312yes—
52C23×C4×C11C2312yes—
53C11×#123—232no—
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⋊C4C2×C418yes—
60C2×C11×C22⋊C4—24no—
61C2×C11×C22⋊C4—24no—
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—41no—
69C2×C11×C22⋊C4—42no—
70C2×C11×C22⋊C4—42no—
71C2×C11×C22⋊C4—42no—
72C2×C11×C22⋊C4—42no—
73C2×C11×C22⋊C4—41no—
74C2×C11×C22⋊C4—42no—
75C2×C11×C22⋊C4C2×C418yes—
76C2×C11×C22⋊C4C2×C414yes—
77C2×C11×C22⋊C4D418yes—
78C2×C42×C11—24no—
79C2×C42×C11—24no—
80C2×C42×C11—42no—
81C11×#95—24no—
82C11×#95—24no—
83C11×#95—41no—
84C11×#95—42no—
85C11×#95—42no—
86C11×#95—42no—
87C11×#95—42no—
88C11×#95—42no—
89C11×#95—41no—
90#14506C1111yesmaximal, characteristic, direct product factor, Sylow
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—22no—
95C24×C11—21no—
96C24×C11—21no—
97C24×C11—22no—
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—22no—
101C24×C11—22no—
102C24×C11—22no—
103C24×C11—21no—
104C24×C11—21no—
105C24×C11—22no—
106C24×C11C22×C412yes—
107C24×C11C22×C412yes—
108C24×C11C2×D414yes—
109C24×C11C2411yescharacteristic
110C2×D4×C11—28no—
111C2×D4×C11—44no—
112C2×D4×C11—44no—
113C2×D4×C11—48no—
114C2×D4×C11—48no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—28no—
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—22no—
129C22×C4×C11—22no—
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—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—44no—
157C22×C4×C11—44no—
158C22×C4×C11—48no—
159C22×C4×C11—48no—
160C22×C4×C11C22×C414yes—
161C22×C4×C11C22×C412yes—
162C22×C4×C11C22×C414yes—
163C22×C4×C11C2×D414yes—
164C22×C4×C11C2×D414yes—
165C22×C4×C11#4114yes—
166C22×C4×C11#4114yes—
167C11×C4⋊C4—216no—
168C11×C4⋊C4—48no—
169C11×C22⋊C4—216no—
170C11×C22⋊C4—44no—
171C11×C22⋊C4—48no—
172C11×C22⋊C4—48no—
173C11×C22⋊C4—48no—
174C11×C22⋊C4—44no—
175C11×C22⋊C4C22⋊C4116yescomplemented
176C42×C11—48no—
177C22×#123C2×C1111yescharacteristic
178C2×#388C2×C1112yescomplemented
179#1445C2×C1112yescomplemented
180#1439C2×C1112yescomplemented
181#1438C2×C1111yescharacteristic
182#1438C2×C1111yescharacteristic
183#1437C2×C1112yescomplemented
184C4⋊#95C2×C1112yescomplemented
185C22⋊#95C2×C1112yescomplemented
186C23×C11—24no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—24no—
190C23×C11—24no—
191C23×C11—24no—
192C23×C11—24no—
193C23×C11—24no—
194C23×C11—24no—
195C23×C11—24no—
196C23×C11—22no—
197C23×C11—24no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—24no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—41no—
206C23×C11—42no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—42no—
210C23×C11—41no—
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—41no—
222C23×C11—42no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—42no—
226C23×C11—41no—
227C23×C11C2×C22⋊C414yes—
228C23×C11C23×C411yescharacteristic
229C23×C11C22×D412yes—
230C23×C11C2×#4112yes—
231C23×C11C2×#4112yes—
232C23×C11H(5,𝔽2)12yes—
233C23×C11H(5,𝔽2)11yescharacteristic
234C23×C11H(5,𝔽2)11yescharacteristic
235C23×C11H(5,𝔽2)12yes—
236C23×C112−1+412yes—
237D4×C11—416no—
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—24no—
245C2×C4×C11—22no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—416no—
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—
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×C11C2×C22⋊C418yes—
286C23×D4C22×C1111yescharacteristic
287C24×C4C22×C1111yescharacteristic
288C2×#123—28no—
289C2×#123C4×C1118yescomplemented
290C22×C4⋊C4C22×C1112yes—
291C22×C4⋊C4C22×C1112yes—
292C22×C22⋊C4C22×C1112yes—
293C22×C22⋊C4C22×C1112yes—
294C22×C22⋊C4C22×C1111yescharacteristic
295C22×C22⋊C4C22×C1112yes—
296C22×C22⋊C4C22×C1112yes—
297C22×C22⋊C4C22×C1111yescharacteristic
298C22×C22⋊C4C22×C1111yescharacteristic
299C22×C42C22×C1112yes—
300#388—28no—
301C2×#95C22×C1112yes—
302C2×#95C22×C1112yes—
303C2×#95C22×C1112yes—
304C2×#95C22×C1112yes—
305C2×#95C22×C1112yes—
306C2×#95C22×C1112yes—
307C2×#95C22×C1111yescharacteristic
308C2×#95C22×C1112yes—
309C2×#95C22×C1111yescharacteristic
310C22×C11—24no—
311C22×C11—28no—
312C22×C11—44no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—44no—
316C22×C11—44no—
317C22×C11—44no—
318C22×C11—44no—
319C22×C11—42no—
320C22×C11—44no—
321C22×C11—44no—
322C22×C11—42no—
323C22×C11—42no—
324C22×C11—82no—
325C22×C11—82no—
326C22×C11—82no—
327C22×C11—82no—
328C22×C11C22×C22⋊C411yescharacteristic
329C22×C11C4×#4112yes—
330C22×C11#51811yescharacteristic
331C22×C11#51811yescharacteristic
332C22×C11#52012yes—
333C22×C11#53512yes—
334C22×C11#53512yes—
335C22×C11#53812yes—
336C22×C11#53912yes—
337C22×C11#54012yes—
338C22×C11#54212yes—
339C22×C11#54612yes—
340C22×C11#54612yes—
341C22×C11#54712yes—
342C22×C11#54712yes—
343C22×C11#55111yescharacteristic
344C22×C11#55312yes—
345C22×C11#55911yescharacteristic
346C22×C11#56011yescharacteristic
347C22×C11#56212yes—
348C22×C11#56311yescharacteristic
349C4×C11—28no—
350C4×C11—44no—
351C4×C11—42no—
352C4×C11—44no—
353C4×C11—44no—
354C4×C11—82no—
355C4×C11—82no—
356C25C23×C1111yescharacteristic
357C25C23×C1111yescharacteristic
358C22×D4—24no—
359C22×D4—42no—
360C22×D4—41no—
361C22×D4—41no—
362C22×D4C2×C4×C1114yes—
363C23×C4—24no—
364C23×C4—42no—
365C23×C4—41no—
366C23×C4—41no—
367C23×C4C2×C4×C1114yes—
368C23×C4C23×C1112yes—
369C23×C4C23×C1112yes—
370C23×C4C23×C1112yes—
371C23×C4C23×C1111yescharacteristic
372C23×C4C23×C1112yes—
373C23×C4C23×C1112yes—
374C23×C4C23×C1112yes—
375#123—232no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—42no—
381C2×C4⋊C4C2×C4×C1118yes—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—41no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—41no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4C2×C4×C1118yes—
398C2×C22⋊C4C2×C4×C1114yes—
399C2×C22⋊C4D4×C1118yes—
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—42no—
403#95—24no—
404#95—24no—
405#95—41no—
406#95—42no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—42no—
411#95—41no—
412C2×C11—44no—
413C2×C11—82no—
414C2×C11#230911yescharacteristic
415C2×C11#233512yes—
416C2×C11#233912yes—
417C2×C11#237411yescharacteristic
418C2×C11#237611yescharacteristic
419C2×C11#270312yes—
420C2×C11#270612yes—
421C2×C11#271012yes—
422C2×C11#271812yes—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—21no—
428C24—21no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—21no—
436C24—21no—
437C24—22no—
438C24C22×C4×C1112yes—
439C24C22×C4×C1112yes—
440C24C2×D4×C1114yes—
441C24C24×C1111yescharacteristic
442C2×D4—28no—
443C2×D4—44no—
444C2×D4—44no—
445C2×D4—48no—
446C2×D4—48no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—28no—
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—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
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—44no—
489C22×C4—44no—
490C22×C4—48no—
491C22×C4—48no—
492C22×C4C22×C4×C1114yes—
493C22×C4C22×C4×C1112yes—
494C22×C4C22×C4×C1114yes—
495C22×C4C2×D4×C1114yes—
496C22×C4C2×D4×C1114yes—
497C22×C4C11×#4114yes—
498C22×C4C11×#4114yes—
499C4⋊C4—216no—
500C4⋊C4—48no—
501C22⋊C4—216no—
502C22⋊C4—44no—
503C22⋊C4—48no—
504C22⋊C4—48no—
505C22⋊C4—48no—
506C22⋊C4—44no—
507C22⋊C4C11×C22⋊C4116yescomplemented
508C42—48no—
509C11#1450611yescharacteristic, direct product factor, Sylow
510C23—24no—
511C23—22no—
512C23—22no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—22no—
521C23—24no—
522C23—22no—
523C23—22no—
524C23—24no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—41no—
530C23—42no—
531C23—41no—
532C23—41no—
533C23—42no—
534C23—41no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—41no—
546C23—42no—
547C23—41no—
548C23—41no—
549C23—42no—
550C23—41no—
551C23C2×C11×C22⋊C414yes—
552C23C23×C4×C1111yescharacteristic
553C23C22×D4×C1112yes—
554C23C2×C11×#4112yes—
555C23C2×C11×#4112yes—
556C23C11×H(5,𝔽2)12yes—
557C23C11×H(5,𝔽2)11yescharacteristic
558C23C11×H(5,𝔽2)11yescharacteristic
559C23C11×H(5,𝔽2)12yes—
560C23C11×2−1+412yes—
561D4—416no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—416no—
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—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
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×C4C2×C11×C22⋊C418yes—
610C22—24no—
611C22—28no—
612C22—44no—
613C22—44no—
614C22—44no—
615C22—44no—
616C22—44no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—44no—
621C22—44no—
622C22—42no—
623C22—42no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22C22×C11×C22⋊C411yescharacteristic
629C22C4×C11×#4112yes—
630C22C11×#51811yescharacteristic
631C22C11×#51811yescharacteristic
632C22C11×#52012yes—
633C22C11×#53512yes—
634C22C11×#53512yes—
635C22C11×#53812yes—
636C22C11×#53912yes—
637C22C11×#54012yes—
638C22C11×#54212yes—
639C22C11×#54612yes—
640C22C11×#54612yes—
641C22C11×#54712yes—
642C22C11×#54712yes—
643C22C11×#55111yescharacteristic
644C22C11×#55312yes—
645C22C11×#55911yescharacteristic
646C22C11×#56011yescharacteristic
647C22C11×#56212yes—
648C22C11×#56311yescharacteristic
649C4—28no—
650C4—44no—
651C4—44no—
652C4—44no—
653C4—42no—
654C4—82no—
655C4—82no—
656C2—44no—
657C2—82no—
658C2C11×#230911yescharacteristic
659C2C11×#233512yes—
660C2C11×#233912yes—
661C2C11×#237411yescharacteristic
662C2C11×#237611yescharacteristic
663C2C11×#270312yes—
664C2C11×#270612yes—
665C2C11×#271012yes—
666C2C11×#271812yes—
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. C2×C11×#388C2semidirect
3. C11×#1445C2semidirect
4. C11×#1439C2semidirect
7. C11×#1437C2semidirect
8. C11×C4⋊#95C2semidirect
9. C11×C22⋊#95C2semidirect
13. C2×C11×#123C4semidirect
90. #14506C11direct (N × H)
175. C11×C22⋊C4C22⋊C4semidirect
178. C2×#388C2×C11semidirect
179. #1445C2×C11semidirect
180. #1439C2×C11semidirect
183. #1437C2×C11semidirect
184. C4⋊#95C2×C11semidirect
185. C22⋊#95C2×C11semidirect
289. C2×#123C4×C11semidirect
507. C22⋊C4C11×C22⋊C4semidirect
509. C11#14506direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1232
C2×C11×#3882
C11×#14452
C11×#14392
C11×#14382
C11×#14372
C11×C4⋊#952
C11×C22⋊#952
#1450611