Finite Group Databasebeta

← C11×#14571 #14591764

Subgroups — C11×#14571 #14591764

Order 2816.

1966 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#394C211yesmaximal, characteristic
2C2×C11×#388C212yesmaximal, complemented
3C2×C11×#386C212yesmaximal
4C11×#1445C211yesmaximal, characteristic, complemented
5C11×#1442C212yesmaximal, complemented
6C11×#1439C212yesmaximal, complemented
7C11×#1436C211yesmaximal, characteristic, complemented
8C11×C22⋊#95C212yesmaximal, complemented
9C11×C22⋊#95C212yesmaximal, complemented
10C23×D4×C11C2211yescharacteristic
11C24×C4×C11C2212yes—
12C22×C11×C4⋊C4C2212yes—
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2212yes—
15C22×C11×C22⋊C4C2212yes—
16C22×C11×C22⋊C4C2212yes—
17C22×C11×C22⋊C4C2212yes—
18C22×C11×C22⋊C4C2212yes—
19C22×C42×C11C2211yescharacteristic
20C11×#394C418yescomplemented
21C11×#388—28no—
22C11×#386—28no—
23C2×C11×#95C2212yes—
24C2×C11×#95C2212yes—
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27C2×C11×#95C2212yes—
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2212yes—
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2212yes—
32C2×C11×#95C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
34C25×C11C2312yes—
35C22×D4×C11—24no—
36C22×D4×C11—24no—
37C22×D4×C11—41no—
38C22×D4×C11—41no—
39C22×D4×C11C2×C414yes—
40C23×C4×C11—24no—
41C23×C4×C11—24no—
42C23×C4×C11—24no—
43C23×C4×C11—42no—
44C23×C4×C11—42no—
45C23×C4×C11—42no—
46C23×C4×C11—42no—
47C23×C4×C11C2312yes—
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2312yes—
53C23×C4×C11C2312yes—
54C23×C4×C11C2312yes—
55C2×C11×C4⋊C4—24no—
56C2×C11×C4⋊C4—41no—
57C2×C11×C4⋊C4—41no—
58C2×C11×C4⋊C4—42no—
59C2×C11×C4⋊C4—42no—
60C2×C11×C4⋊C4C2×C414yescomplemented
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—42no—
68C2×C11×C22⋊C4—42no—
69C2×C11×C22⋊C4—42no—
70C2×C11×C22⋊C4—42no—
71C2×C11×C22⋊C4—42no—
72C2×C11×C22⋊C4—42no—
73C2×C11×C22⋊C4C2×C418yescomplemented
74C2×C11×C22⋊C4C2×C418yescomplemented
75C2×C11×C22⋊C4D418yes—
76C2×C42×C11—24no—
77C2×C42×C11—41no—
78C11×#95—24no—
79C11×#95—24no—
80C11×#95—24no—
81C11×#95—24no—
82C11×#95—24no—
83C11×#95—42no—
84C11×#95—41no—
85C11×#95—42no—
86C11×#95—41no—
87C11×#95—41no—
88C11×#95C2×C414yescomplemented
89#14571C1111yesmaximal, 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×C11C22×C414yes—
103C24×C11C2×D414yes—
104C24×C11#4114yes—
105C24×C11C2411yescharacteristic
106C2×D4×C11—216no—
107C2×D4×C11—44no—
108C2×D4×C11—44no—
109C2×D4×C11—48no—
110C2×D4×C11—44no—
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—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
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—21no—
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—21no—
144C22×C4×C11—21no—
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—48no—
155C22×C4×C11—48no—
156C22×C4×C11—48no—
157C22×C4×C11—48no—
158C22×C4×C11—48no—
159C22×C4×C11—48no—
160C22×C4×C11—48no—
161C22×C4×C11C22×C414yes—
162C22×C4×C11C22×C412yes—
163C22×C4×C11C22×C412yes—
164C22×C4×C11C22×C412yes—
165C22×C4×C11C2×D414yes—
166C22×C4×C11C2×D414yes—
167C22×C4×C11#4114yes—
168C11×C4⋊C4—44no—
169C11×C4⋊C4—48no—
170C11×C22⋊C4—216no—
171C11×C22⋊C4—48no—
172C11×C22⋊C4—48no—
173C11×C22⋊C4—48no—
174C11×C22⋊C4—48no—
175C42×C11—44no—
176C2×#394C2×C1111yescharacteristic
177C2×#388C2×C1112yescomplemented
178C2×#386C2×C1112yes—
179#1445C2×C1111yescharacteristic, complemented
180#1442C2×C1112yescomplemented
181#1439C2×C1112yescomplemented
182#1436C2×C1111yescharacteristic, complemented
183C22⋊#95C2×C1112yescomplemented
184C22⋊#95C2×C1112yescomplemented
185C23×C11—24no—
186C23×C11—24no—
187C23×C11—24no—
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—42no—
204C23×C11—42no—
205C23×C11—42no—
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×C11C4×D418yes—
220C23×C11C23×C411yescharacteristic
221C23×C11C22×D412yes—
222C23×C11C2×#4112yes—
223C23×C11C2×#4112yes—
224C23×C11H(5,𝔽2)12yes—
225C23×C11H(5,𝔽2)11yescharacteristic
226C23×C11H(5,𝔽2)11yescharacteristic
227C23×C11H(5,𝔽2)12yes—
228C23×C112−1+412yes—
229D4×C11—416no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
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—24no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—432no—
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—41no—
263C2×C4×C11—41no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
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—
281C23×D4C22×C1111yescharacteristic
282C24×C4C22×C1112yes—
283C22×C4⋊C4C22×C1112yes—
284C22×C4⋊C4C22×C1111yescharacteristic
285C22×C22⋊C4C22×C1112yes—
286C22×C22⋊C4C22×C1112yes—
287C22×C22⋊C4C22×C1112yes—
288C22×C22⋊C4C22×C1112yes—
289C22×C22⋊C4C22×C1112yes—
290C22×C42C22×C1111yescharacteristic
291#394C4×C1118yescomplemented
292#388—28no—
293#386—28no—
294C2×#95C22×C1112yes—
295C2×#95C22×C1112yes—
296C2×#95C22×C1112yes—
297C2×#95C22×C1112yes—
298C2×#95C22×C1112yes—
299C2×#95C22×C1111yescharacteristic
300C2×#95C22×C1112yes—
301C2×#95C22×C1111yescharacteristic
302C2×#95C22×C1112yes—
303C2×#95C22×C1111yescharacteristic
304C2×#95C22×C1111yescharacteristic
305C22×C11—28no—
306C22×C11—28no—
307C22×C11—28no—
308C22×C11—44no—
309C22×C11—44no—
310C22×C11—44no—
311C22×C11—44no—
312C22×C11—44no—
313C22×C11—44no—
314C22×C11—44no—
315C22×C11—44no—
316C22×C11—44no—
317C22×C11—44no—
318C22×C11—44no—
319C22×C11—44no—
320C22×C11C2×C4×D412yes—
321C22×C11C4×#4111yescharacteristic
322C22×C11#51811yescharacteristic
323C22×C11#51811yescharacteristic
324C22×C11#52012yes—
325C22×C11#53412yes—
326C22×C11#53712yes—
327C22×C11#53812yes—
328C22×C11#53812yes—
329C22×C11#53912yes—
330C22×C11#54012yes—
331C22×C11D4211yescharacteristic
332C22×C11#54612yes—
333C22×C11#54612yes—
334C22×C11#54712yes—
335C22×C11#55111yescharacteristic
336C22×C11#55112yes—
337C22×C11#55212yes—
338C22×C11H(3,𝔽4)11yescharacteristic
339C22×C11#56212yes—
340C22×C11#56311yescharacteristic
341C4×C11—44no—
342C4×C11—42no—
343C4×C11—42no—
344C4×C11—42no—
345C4×C11—44no—
346C4×C11—44no—
347C4×C11—44no—
348C4×C11—82no—
349C25C23×C1112yes—
350C22×D4—24no—
351C22×D4—24no—
352C22×D4—41no—
353C22×D4—41no—
354C22×D4C2×C4×C1114yes—
355C23×C4—24no—
356C23×C4—24no—
357C23×C4—24no—
358C23×C4—42no—
359C23×C4—42no—
360C23×C4—42no—
361C23×C4—42no—
362C23×C4C23×C1112yes—
363C23×C4C23×C1112yes—
364C23×C4C23×C1111yescharacteristic
365C23×C4C23×C1111yescharacteristic
366C23×C4C23×C1111yescharacteristic
367C23×C4C23×C1112yes—
368C23×C4C23×C1112yes—
369C23×C4C23×C1112yes—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—41no—
372C2×C4⋊C4—41no—
373C2×C4⋊C4—42no—
374C2×C4⋊C4—42no—
375C2×C4⋊C4C2×C4×C1114yescomplemented
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4C2×C4×C1118yescomplemented
389C2×C22⋊C4C2×C4×C1118yescomplemented
390C2×C22⋊C4D4×C1118yes—
391C2×C42—24no—
392C2×C42—41no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—42no—
399#95—41no—
400#95—42no—
401#95—41no—
402#95—41no—
403#95C2×C4×C1114yescomplemented
404C2×C11—48no—
405C2×C11#232512yes—
406C2×C11#233311yescharacteristic
407C2×C11#235811yescharacteristic
408C2×C11#235912yes—
409C2×C11#237911yescharacteristic
410C2×C11#267112yes—
411C2×C11#268412yes—
412C2×C11#269512yes—
413C2×C11#274312yes—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24C22×C4×C1114yes—
427C24C2×D4×C1114yes—
428C24C11×#4114yes—
429C24C24×C1111yescharacteristic
430C2×D4—216no—
431C2×D4—44no—
432C2×D4—44no—
433C2×D4—48no—
434C2×D4—44no—
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—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
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—48no—
479C22×C4—48no—
480C22×C4—48no—
481C22×C4—48no—
482C22×C4—48no—
483C22×C4—48no—
484C22×C4—48no—
485C22×C4C22×C4×C1114yes—
486C22×C4C22×C4×C1112yes—
487C22×C4C22×C4×C1112yes—
488C22×C4C22×C4×C1112yes—
489C22×C4C2×D4×C1114yes—
490C22×C4C2×D4×C1114yes—
491C22×C4C11×#4114yes—
492C4⋊C4—44no—
493C4⋊C4—48no—
494C22⋊C4—216no—
495C22⋊C4—48no—
496C22⋊C4—48no—
497C22⋊C4—48no—
498C22⋊C4—48no—
499C42—44no—
500C11#1457111yescharacteristic, direct product factor, Sylow
501C23—24no—
502C23—24no—
503C23—24no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—24no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23C4×D4×C1118yes—
536C23C23×C4×C1111yescharacteristic
537C23C22×D4×C1112yes—
538C23C2×C11×#4112yes—
539C23C2×C11×#4112yes—
540C23C11×H(5,𝔽2)12yes—
541C23C11×H(5,𝔽2)11yescharacteristic
542C23C11×H(5,𝔽2)11yescharacteristic
543C23C11×H(5,𝔽2)12yes—
544C23C11×2−1+412yes—
545D4—416no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—432no—
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—41no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—41no—
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—
597C22—28no—
598C22—28no—
599C22—28no—
600C22—44no—
601C22—44no—
602C22—44no—
603C22—44no—
604C22—44no—
605C22—44no—
606C22—44no—
607C22—44no—
608C22—44no—
609C22—44no—
610C22—44no—
611C22—44no—
612C22C2×C4×D4×C1112yes—
613C22C4×C11×#4111yescharacteristic
614C22C11×#51811yescharacteristic
615C22C11×#51811yescharacteristic
616C22C11×#52012yes—
617C22C11×#53412yes—
618C22C11×#53712yes—
619C22C11×#53812yes—
620C22C11×#53812yes—
621C22C11×#53912yes—
622C22C11×#54012yes—
623C22D42×C1111yescharacteristic
624C22C11×#54612yes—
625C22C11×#54612yes—
626C22C11×#54712yes—
627C22C11×#55112yes—
628C22C11×#55111yescharacteristic
629C22C11×#55212yes—
630C22C11×H(3,𝔽4)11yescharacteristic
631C22C11×#56212yes—
632C22C11×#56311yescharacteristic
633C4—44no—
634C4—44no—
635C4—44no—
636C4—44no—
637C4—42no—
638C4—42no—
639C4—42no—
640C4—82no—
641C2—48no—
642C2C11×#232512yes—
643C2C11×#233311yescharacteristic
644C2C11×#235811yescharacteristic
645C2C11×#235912yes—
646C2C11×#237911yescharacteristic
647C2C11×#267112yes—
648C2C11×#268412yes—
649C2C11×#269512yes—
650C2C11×#274312yes—
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
4. C11×#1445C2semidirect
5. C11×#1442C2semidirect
6. C11×#1439C2semidirect
7. C11×#1436C2semidirect
8. C11×C22⋊#95C2semidirect
9. C11×C22⋊#95C2semidirect
20. C11×#394C4semidirect
60. C2×C11×C4⋊C4C2×C4semidirect
73. C2×C11×C22⋊C4C2×C4semidirect
74. C2×C11×C22⋊C4C2×C4semidirect
88. C11×#95C2×C4semidirect
89. #14571C11direct (N × H)
177. C2×#388C2×C11semidirect
179. #1445C2×C11semidirect
180. #1442C2×C11semidirect
181. #1439C2×C11semidirect
182. #1436C2×C11semidirect
183. C22⋊#95C2×C11semidirect
184. C22⋊#95C2×C11semidirect
291. #394C4×C11semidirect
375. C2×C4⋊C4C2×C4×C11semidirect
388. C2×C22⋊C4C2×C4×C11semidirect
389. C2×C22⋊C4C2×C4×C11semidirect
403. #95C2×C4×C11semidirect
500. C11#14571direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3942
C2×C11×#3882
C2×C11×#3862
C11×#14452
C11×#14422
C11×#14392
C11×#14362
C11×C22⋊#952
#1457111