Finite Group Databasebeta

← C11×#14575 #14591768

Subgroups — C11×#14575 #14591768

Order 2816.

1706 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#393C211yesmaximal, characteristic
2C2×C11×#391C212yesmaximal, complemented
3C2×C11×#385C212yesmaximal
4C11×#1444C212yesmaximal, complemented
5C11×#1442C212yesmaximal, complemented
6C11×#1439C211yesmaximal, characteristic
7C11×#1437C212yesmaximal
8C11×#1434C212yesmaximal, complemented
9C11×C22⋊#95C211yesmaximal, characteristic
10C23×Q8×C11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C22×C11×C4⋊C4C2212yes—
13C22×C11×C4⋊C4C2212yes—
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2212yes—
16C22×C11×C22⋊C4C2212yes—
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C42×C11C2212yes—
20C11×#393C418yescomplemented
21C11×#391—28no—
22C11×#385—28no—
23C2×C11×#95C2212yes—
24C2×C11×#95C2212yes—
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27C2×C11×#95C2212yes—
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2212yes—
30C2×C11×#95C2212yes—
31C2×C11×#95C2212yes—
32C2×C11×#95C2211yescharacteristic
33C2×C11×#95C2212yes—
34C25×C11C2311yescharacteristic
35C22×Q8×C11—24no—
36C22×Q8×C11—24no—
37C22×Q8×C11—41no—
38C22×Q8×C11—41no—
39C22×Q8×C11C2×C414yescomplemented
40C23×C4×C11—22no—
41C23×C4×C11—24no—
42C23×C4×C11—42no—
43C23×C4×C11—41no—
44C23×C4×C11—41no—
45C23×C4×C11C2312yes—
46C23×C4×C11C2312yes—
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2312yes—
50C23×C4×C11C2312yes—
51C23×C4×C11C2312yes—
52C23×C4×C11C2312yes—
53C2×C11×C4⋊C4—24no—
54C2×C11×C4⋊C4—24no—
55C2×C11×C4⋊C4—24no—
56C2×C11×C4⋊C4—42no—
57C2×C11×C4⋊C4—42no—
58C2×C11×C4⋊C4—42no—
59C2×C11×C4⋊C4—42no—
60C2×C11×C4⋊C4—41no—
61C2×C11×C22⋊C4—24no—
62C2×C11×C22⋊C4—24no—
63C2×C11×C22⋊C4—24no—
64C2×C11×C22⋊C4—24no—
65C2×C11×C22⋊C4—41no—
66C2×C11×C22⋊C4—41no—
67C2×C11×C22⋊C4—41no—
68C2×C11×C22⋊C4—41no—
69C2×C11×C22⋊C4—42no—
70C2×C11×C22⋊C4C2×C418yes—
71C2×C11×C22⋊C4C2×C414yes—
72C2×C11×C22⋊C4Q814yescomplemented
73C2×C42×C11—24no—
74C2×C42×C11—24no—
75C2×C42×C11—42no—
76C11×#95—24no—
77C11×#95—24no—
78C11×#95—24no—
79C11×#95—24no—
80C11×#95—42no—
81C11×#95—42no—
82C11×#95—41no—
83C11×#95—42no—
84C11×#95C2×C414yescomplemented
85C11×#95C2×C418yescomplemented
86C11×#95D418yes—
87#14575C1111yesmaximal, characteristic, direct product factor, Sylow
88C24×C11—22no—
89C24×C11—22no—
90C24×C11—21no—
91C24×C11—21no—
92C24×C11—21no—
93C24×C11—22no—
94C24×C11—21no—
95C24×C11—22no—
96C24×C11C22×C412yes—
97C24×C11C2×Q812yes—
98C24×C11#4112yes—
99C24×C11C2411yescharacteristic
100C2×Q8×C11—216no—
101C2×Q8×C11—44no—
102C2×Q8×C11—44no—
103C2×Q8×C11—48no—
104C2×Q8×C11—44no—
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—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—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—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
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—44no—
149C22×C4×C11—48no—
150C22×C4×C11—48no—
151C22×C4×C11—44no—
152C22×C4×C11—44no—
153C22×C4×C11C22×C414yes—
154C22×C4×C11C22×C412yes—
155C22×C4×C11C22×C412yes—
156C22×C4×C11C22×C414yes—
157C22×C4×C11C2×D414yes—
158C22×C4×C11C2×D414yes—
159C22×C4×C11C2×D414yes—
160C22×C4×C11C2×Q814yes—
161C22×C4×C11#4114yes—
162C11×C4⋊C4—48no—
163C11×C4⋊C4—48no—
164C11×C4⋊C4—44no—
165C11×C22⋊C4—216no—
166C11×C22⋊C4—44no—
167C11×C22⋊C4—44no—
168C11×C22⋊C4—48no—
169C42×C11—48no—
170C2×#393C2×C1111yescharacteristic
171C2×#391C2×C1112yescomplemented
172C2×#385C2×C1112yes—
173#1444C2×C1112yescomplemented
174#1442C2×C1112yescomplemented
175#1439C2×C1111yescharacteristic
176#1437C2×C1112yes—
177#1434C2×C1112yescomplemented
178C22⋊#95C2×C1111yescharacteristic
179C23×C11—24no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—24no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—24no—
188C23×C11—24no—
189C23×C11—24no—
190C23×C11—24no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—41no—
196C23×C11—42no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—42no—
200C23×C11—41no—
201C23×C11C4×Q814yes—
202C23×C11C23×C411yescharacteristic
203C23×C11C22×D412yes—
204C23×C11C22×Q811yescharacteristic
205C23×C11C2×#4112yes—
206C23×C11C2×#4111yescharacteristic
207C23×C11H(5,𝔽2)11yescharacteristic
208C23×C11H(5,𝔽2)11yescharacteristic
209C23×C11H(5,𝔽2)11yescharacteristic
210C23×C11H(5,𝔽2)12yes—
211C23×C112−1+411yescharacteristic
212C23×C112−1+412yes—
213Q8×C11—416no—
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—24no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
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—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—416no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—41no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—41no—
252C2×C4×C11—42no—
253C2×C4×C11—41no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—41no—
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×C11C4×D418yes—
267C23×Q8C22×C1111yescharacteristic
268C24×C4C22×C1111yescharacteristic
269C22×C4⋊C4C22×C1112yes—
270C22×C4⋊C4C22×C1112yes—
271C22×C4⋊C4C22×C1111yescharacteristic
272C22×C22⋊C4C22×C1112yes—
273C22×C22⋊C4C22×C1112yes—
274C22×C22⋊C4C22×C1111yescharacteristic
275C22×C22⋊C4C22×C1111yescharacteristic
276C22×C42C22×C1112yes—
277#393C4×C1118yescomplemented
278#391—28no—
279#385—28no—
280C2×#95C22×C1112yes—
281C2×#95C22×C1112yes—
282C2×#95C22×C1112yes—
283C2×#95C22×C1112yes—
284C2×#95C22×C1112yes—
285C2×#95C22×C1111yescharacteristic
286C2×#95C22×C1112yes—
287C2×#95C22×C1112yes—
288C2×#95C22×C1112yes—
289C2×#95C22×C1111yescharacteristic
290C2×#95C22×C1112yes—
291C22×C11—24no—
292C22×C11—28no—
293C22×C11—44no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—44no—
299C22×C11—44no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11C2×C4×D412yes—
303C22×C11C2×C4×Q811yescharacteristic
304C22×C11#51811yescharacteristic
305C22×C11#52011yescharacteristic
306C22×C11#52012yes—
307C22×C11#53512yes—
308C22×C11#53612yes—
309C22×C11#53811yescharacteristic
310C22×C11#53911yescharacteristic
311C22×C11#54212yes—
312C22×C11#54212yes—
313C22×C11#54311yescharacteristic
314C22×C11#54411yescharacteristic
315C22×C11D4211yescharacteristic
316C22×C11#54612yes—
317C22×C11#54612yes—
318C22×C11D4×Q812yes—
319C22×C11#55111yescharacteristic
320C22×C11#55212yes—
321C22×C11#55412yes—
322C22×C11H(3,𝔽4)11yescharacteristic
323C22×C11#56212yes—
324C22×C11#56311yescharacteristic
325C4×C11—28no—
326C4×C11—44no—
327C4×C11—42no—
328C4×C11—42no—
329C4×C11—44no—
330C4×C11—44no—
331C4×C11—44no—
332C4×C11—82no—
333C25C23×C1111yescharacteristic
334C22×Q8—24no—
335C22×Q8—24no—
336C22×Q8—41no—
337C22×Q8—41no—
338C22×Q8C2×C4×C1114yescomplemented
339C23×C4—22no—
340C23×C4—24no—
341C23×C4—42no—
342C23×C4—41no—
343C23×C4—41no—
344C23×C4C23×C1112yes—
345C23×C4C23×C1112yes—
346C23×C4C23×C1111yescharacteristic
347C23×C4C23×C1111yescharacteristic
348C23×C4C23×C1112yes—
349C23×C4C23×C1112yes—
350C23×C4C23×C1112yes—
351C23×C4C23×C1112yes—
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—42no—
359C2×C4⋊C4—41no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4—41no—
366C2×C22⋊C4—41no—
367C2×C22⋊C4—41no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4C2×C4×C1118yes—
370C2×C22⋊C4C2×C4×C1114yes—
371C2×C22⋊C4Q8×C1114yescomplemented
372C2×C42—24no—
373C2×C42—24no—
374C2×C42—42no—
375#95—24no—
376#95—24no—
377#95—24no—
378#95—24no—
379#95—42no—
380#95—42no—
381#95—41no—
382#95—42no—
383#95C2×C4×C1114yescomplemented
384#95C2×C4×C1118yescomplemented
385#95D4×C1118yes—
386C2×C11—44no—
387C2×C11#232612yes—
388C2×C11#232911yescharacteristic
389C2×C11#235811yescharacteristic
390C2×C11#236012yes—
391C2×C11#237911yescharacteristic
392C2×C11#267011yescharacteristic
393C2×C11#267711yescharacteristic
394C2×C11#268712yes—
395C2×C11#269212yes—
396C2×C11#276311yescharacteristic
397C2×C11#276411yescharacteristic
398C24—22no—
399C24—22no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—22no—
404C24—21no—
405C24—22no—
406C24C22×C4×C1112yes—
407C24C2×Q8×C1112yes—
408C24C11×#4112yes—
409C24C24×C1111yescharacteristic
410C2×Q8—216no—
411C2×Q8—44no—
412C2×Q8—44no—
413C2×Q8—48no—
414C2×Q8—44no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
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—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—44no—
459C22×C4—48no—
460C22×C4—48no—
461C22×C4—44no—
462C22×C4—44no—
463C22×C4C22×C4×C1114yes—
464C22×C4C22×C4×C1112yes—
465C22×C4C22×C4×C1112yes—
466C22×C4C22×C4×C1114yes—
467C22×C4C2×D4×C1114yes—
468C22×C4C2×D4×C1114yes—
469C22×C4C2×D4×C1114yes—
470C22×C4C2×Q8×C1114yes—
471C22×C4C11×#4114yes—
472C4⋊C4—48no—
473C4⋊C4—48no—
474C4⋊C4—44no—
475C22⋊C4—216no—
476C22⋊C4—44no—
477C22⋊C4—44no—
478C22⋊C4—48no—
479C42—48no—
480C11#1457511yescharacteristic, direct product factor, Sylow
481C23—24no—
482C23—22no—
483C23—22no—
484C23—24no—
485C23—22no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—24no—
490C23—24no—
491C23—24no—
492C23—24no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—41no—
498C23—42no—
499C23—41no—
500C23—41no—
501C23—42no—
502C23—41no—
503C23C4×Q8×C1114yes—
504C23C23×C4×C1111yescharacteristic
505C23C22×D4×C1112yes—
506C23C22×Q8×C1111yescharacteristic
507C23C2×C11×#4112yes—
508C23C2×C11×#4111yescharacteristic
509C23C11×H(5,𝔽2)11yescharacteristic
510C23C11×H(5,𝔽2)11yescharacteristic
511C23C11×H(5,𝔽2)11yescharacteristic
512C23C11×H(5,𝔽2)12yes—
513C23C11×2−1+411yescharacteristic
514C23C11×2−1+412yes—
515Q8—416no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—416no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—41no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4C4×D4×C1118yes—
569C22—24no—
570C22—28no—
571C22—42no—
572C22—42no—
573C22—42no—
574C22—44no—
575C22—44no—
576C22—42no—
577C22—42no—
578C22—44no—
579C22—42no—
580C22C2×C4×D4×C1112yes—
581C22C2×C4×Q8×C1111yescharacteristic
582C22C11×#51811yescharacteristic
583C22C11×#52012yes—
584C22C11×#52011yescharacteristic
585C22C11×#53512yes—
586C22C11×#53612yes—
587C22C11×#53811yescharacteristic
588C22C11×#53911yescharacteristic
589C22C11×#54212yes—
590C22C11×#54212yes—
591C22C11×#54311yescharacteristic
592C22C11×#54411yescharacteristic
593C22D42×C1111yescharacteristic
594C22C11×#54612yes—
595C22C11×#54612yes—
596C22D4×Q8×C1112yes—
597C22C11×#55111yescharacteristic
598C22C11×#55212yes—
599C22C11×#55412yes—
600C22C11×H(3,𝔽4)11yescharacteristic
601C22C11×#56212yes—
602C22C11×#56311yescharacteristic
603C4—28no—
604C4—42no—
605C4—44no—
606C4—44no—
607C4—44no—
608C4—44no—
609C4—42no—
610C4—82no—
611C2—44no—
612C2C11×#232612yes—
613C2C11×#232911yescharacteristic
614C2C11×#235811yescharacteristic
615C2C11×#236012yes—
616C2C11×#237911yescharacteristic
617C2C11×#267011yescharacteristic
618C2C11×#267711yescharacteristic
619C2C11×#268712yes—
620C2C11×#269212yes—
621C2C11×#276311yescharacteristic
622C2C11×#276411yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC25×C11C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#391C2semidirect
4. C11×#1444C2semidirect
5. C11×#1442C2semidirect
8. C11×#1434C2semidirect
20. C11×#393C4semidirect
39. C22×Q8×C11C2×C4semidirect
72. C2×C11×C22⋊C4Q8semidirect
84. C11×#95C2×C4semidirect
85. C11×#95C2×C4semidirect
87. #14575C11direct (N × H)
171. C2×#391C2×C11semidirect
173. #1444C2×C11semidirect
174. #1442C2×C11semidirect
177. #1434C2×C11semidirect
277. #393C4×C11semidirect
338. C22×Q8C2×C4×C11semidirect
371. C2×C22⋊C4Q8×C11semidirect
383. #95C2×C4×C11semidirect
384. #95C2×C4×C11semidirect
480. C11#14575direct (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×#3912
C2×C11×#3852
C11×#14442
C11×#14422
C11×#14392
C11×#14372
C11×#14342
C11×C22⋊#952
#1457511