Finite Group Databasebeta

← C11×#13831 #14591024

Subgroups — C11×#13831 #14591024

Order 2816.

1630 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#388C212yesmaximal
2C2×C11×#385C211yesmaximal, characteristic
3C11×#1437C211yesmaximal, characteristic
4C11×#1437C211yesmaximal, characteristic
5C11×#1436C212yesmaximal, complemented
6C11×#1436C212yesmaximal, complemented
7C11×C4⋊#95C212yesmaximal, complemented
8C11×#1434C212yesmaximal, complemented
9C11×C22⋊#95C212yesmaximal
10C24×C4×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2212yes—
12C22×C11×C4⋊C4C2212yes—
13C22×C11×C22⋊C4C2212yes—
14C22×C11×C22⋊C4C2212yes—
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×C42×C11C2212yes—
20C11×#388C4116yescomplemented
21C11×#385C418yescomplemented
22C2×C11×#95C2212yes—
23C2×C11×#95C2212yes—
24C2×C11×#95C2212yes—
25C2×C11×#95C2212yes—
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2212yes—
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2212yes—
30C2×C11×#95C2212yes—
31C2×C11×#95C2212yes—
32C2×C11×#95C2212yes—
33C25×C11C2311yescharacteristic
34C23×C4×C11—41no—
35C23×C4×C11—41no—
36C23×C4×C11—42no—
37C23×C4×C11—42no—
38C23×C4×C11C2×C414yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2312yes—
46C23×C4×C11C2312yes—
47C2×C11×C4⋊C4—42no—
48C2×C11×C4⋊C4—42no—
49C2×C11×C4⋊C4—42no—
50C2×C11×C4⋊C4—42no—
51C2×C11×C4⋊C4C2×C418yes—
52C2×C11×C4⋊C4C2×C418yescomplemented
53C2×C11×C22⋊C4—42no—
54C2×C11×C22⋊C4—41no—
55C2×C11×C22⋊C4—41no—
56C2×C11×C22⋊C4—42no—
57C2×C11×C22⋊C4—42no—
58C2×C11×C22⋊C4—42no—
59C2×C11×C22⋊C4C2×C414yes—
60C2×C11×C22⋊C4C2×C418yes—
61C2×C11×C22⋊C4C2×C418yes—
62C2×C11×C22⋊C4C2×C414yes—
63C2×C11×C22⋊C4C2×C418yes—
64C2×C42×C11—42no—
65C2×C42×C11—42no—
66C2×C42×C11—41no—
67C2×C42×C11—41no—
68C2×C42×C11—42no—
69C2×C42×C11—42no—
70C2×C42×C11C2×C418yescomplemented
71C11×#95—41no—
72C11×#95—41no—
73C11×#95—42no—
74C11×#95—42no—
75C11×#95—42no—
76C11×#95—42no—
77C11×#95—42no—
78C11×#95—42no—
79C11×#95C2×C418yes—
80C11×#95C2×C418yescomplemented
81C11×#95C2×C418yescomplemented
82#13831C1111yesmaximal, characteristic, direct product factor, Sylow
83C24×C11—22no—
84C24×C11—21no—
85C24×C11—21no—
86C24×C11—22no—
87C24×C11—22no—
88C24×C11—22no—
89C24×C11—22no—
90C24×C11C22×C414yes—
91C24×C11C22×C412yes—
92C24×C11C2411yescharacteristic
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
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—21no—
120C22×C4×C11—21no—
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—48no—
136C22×C4×C11—44no—
137C22×C4×C11—44no—
138C22×C4×C11—48no—
139C22×C4×C11—44no—
140C22×C4×C11C22×C412yes—
141C22×C4×C11C22×C414yes—
142C22×C4×C11C22×C414yes—
143C22×C4×C11C22×C414yes—
144C22×C4×C11C22×C414yes—
145C22×C4×C11C22×C414yes—
146C22×C4×C11C22×C412yes—
147C22×C4×C11C22×C414yes—
148C22×C4×C11C22×C414yes—
149C22×C4×C11C22×C414yes—
150C11×C4⋊C4—48no—
151C11×C4⋊C4—48no—
152C11×C22⋊C4—48no—
153C11×C22⋊C4—48no—
154C11×C22⋊C4—44no—
155C11×C22⋊C4C42116yescomplemented
156C42×C11—48no—
157C42×C11—44no—
158C42×C11—44no—
159C2×#388C2×C1112yes—
160C2×#385C2×C1111yescharacteristic
161#1437C2×C1111yescharacteristic
162#1437C2×C1111yescharacteristic
163#1436C2×C1112yescomplemented
164#1436C2×C1112yescomplemented
165C4⋊#95C2×C1112yescomplemented
166#1434C2×C1112yescomplemented
167C22⋊#95C2×C1112yes—
168C23×C11—22no—
169C23×C11—24no—
170C23×C11—24no—
171C23×C11—24no—
172C23×C11—22no—
173C23×C11—24no—
174C23×C11—24no—
175C23×C11—24no—
176C23×C11—24no—
177C23×C11—24no—
178C23×C11—41no—
179C23×C11—42no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—41no—
187C23×C11—42no—
188C23×C11C2×C4214yes—
189C23×C11C23×C411yescharacteristic
190C23×C11C23×C412yes—
191C23×C11H(5,𝔽2)12yes—
192C23×C11H(5,𝔽2)12yes—
193C23×C11H(5,𝔽2)12yes—
194C23×C11H(5,𝔽2)11yescharacteristic
195C23×C11H(5,𝔽2)11yescharacteristic
196C23×C112−1+412yes—
197C23×C112−1+412yes—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
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—24no—
223C2×C4×C11—416no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11—41no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—41no—
236C2×C4×C11—42no—
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—42no—
248C2×C4×C11—41no—
249C2×C4×C11—42no—
250C2×C4×C11C2×C4218yes—
251C24×C4C22×C1111yescharacteristic
252C22×C4⋊C4C22×C1112yes—
253C22×C4⋊C4C22×C1112yes—
254C22×C22⋊C4C22×C1112yes—
255C22×C22⋊C4C22×C1112yes—
256C22×C22⋊C4C22×C1111yescharacteristic
257C22×C22⋊C4C22×C1111yescharacteristic
258C22×C42C22×C1111yescharacteristic
259C22×C42C22×C1111yescharacteristic
260C22×C42C22×C1112yes—
261#388C4×C11116yescomplemented
262#385C4×C1118yescomplemented
263C2×#95C22×C1112yes—
264C2×#95C22×C1112yes—
265C2×#95C22×C1112yes—
266C2×#95C22×C1112yes—
267C2×#95C22×C1111yescharacteristic
268C2×#95C22×C1112yes—
269C2×#95C22×C1111yescharacteristic
270C2×#95C22×C1112yes—
271C2×#95C22×C1112yes—
272C2×#95C22×C1112yes—
273C2×#95C22×C1112yes—
274C22×C11—24no—
275C22×C11—28no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11—44no—
279C22×C11—44no—
280C22×C11—44no—
281C22×C11—44no—
282C22×C11—44no—
283C22×C11C22×C4211yescharacteristic
284C22×C11#51811yescharacteristic
285C22×C11#51812yes—
286C22×C11#51812yes—
287C22×C11#51812yes—
288C22×C11#51911yescharacteristic
289C22×C11#52012yes—
290C22×C11#52012yes—
291C22×C11#52012yes—
292C22×C11#52012yes—
293C22×C11#52012yes—
294C22×C11#56011yescharacteristic
295C22×C11#56012yes—
296C22×C11#56011yescharacteristic
297C22×C11H(3,𝔽4)11yescharacteristic
298C22×C11#56212yes—
299C22×C11#56212yes—
300C22×C11#56212yes—
301C22×C11#56312yes—
302C22×C11#56311yescharacteristic
303C22×C11#56312yes—
304C4×C11—28no—
305C4×C11—42no—
306C4×C11—44no—
307C4×C11—44no—
308C4×C11—42no—
309C4×C11—44no—
310C4×C11—44no—
311C4×C11—44no—
312C25C23×C1111yescharacteristic
313C23×C4—41no—
314C23×C4—41no—
315C23×C4—42no—
316C23×C4—42no—
317C23×C4C2×C4×C1114yes—
318C23×C4C23×C1111yescharacteristic
319C23×C4C23×C1112yes—
320C23×C4C23×C1112yes—
321C23×C4C23×C1112yes—
322C23×C4C23×C1111yescharacteristic
323C23×C4C23×C1112yes—
324C23×C4C23×C1112yes—
325C23×C4C23×C1112yes—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4C2×C4×C1118yes—
331C2×C4⋊C4C2×C4×C1118yescomplemented
332C2×C22⋊C4—42no—
333C2×C22⋊C4—41no—
334C2×C22⋊C4—41no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4C2×C4×C1114yes—
339C2×C22⋊C4C2×C4×C1118yes—
340C2×C22⋊C4C2×C4×C1118yes—
341C2×C22⋊C4C2×C4×C1114yes—
342C2×C22⋊C4C2×C4×C1118yes—
343C2×C42—42no—
344C2×C42—42no—
345C2×C42—41no—
346C2×C42—41no—
347C2×C42—42no—
348C2×C42—42no—
349C2×C42C2×C4×C1118yescomplemented
350#95—41no—
351#95—41no—
352#95—42no—
353#95—42no—
354#95—42no—
355#95—42no—
356#95—42no—
357#95—42no—
358#95C2×C4×C1118yes—
359#95C2×C4×C1118yescomplemented
360#95C2×C4×C1118yescomplemented
361C2×C11—44no—
362C2×C11#227411yescharacteristic
363C2×C11#227512yes—
364C2×C11#237511yescharacteristic
365C2×C11#237611yescharacteristic
366C2×C11#237612yes—
367C2×C11#237712yes—
368C2×C11#237812yes—
369C2×C11#237912yes—
370C2×C11#238312yes—
371C24—22no—
372C24—21no—
373C24—21no—
374C24—22no—
375C24—22no—
376C24—22no—
377C24—22no—
378C24C22×C4×C1114yes—
379C24C22×C4×C1112yes—
380C24C24×C1111yescharacteristic
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
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—48no—
424C22×C4—44no—
425C22×C4—48no—
426C22×C4—44no—
427C22×C4—44no—
428C22×C4C22×C4×C1112yes—
429C22×C4C22×C4×C1114yes—
430C22×C4C22×C4×C1114yes—
431C22×C4C22×C4×C1114yes—
432C22×C4C22×C4×C1114yes—
433C22×C4C22×C4×C1114yes—
434C22×C4C22×C4×C1112yes—
435C22×C4C22×C4×C1114yes—
436C22×C4C22×C4×C1114yes—
437C22×C4C22×C4×C1114yes—
438C4⋊C4—48no—
439C4⋊C4—48no—
440C22⋊C4—48no—
441C22⋊C4—48no—
442C22⋊C4—44no—
443C22⋊C4C42×C11116yescomplemented
444C42—48no—
445C42—44no—
446C42—44no—
447C11#1383111yescharacteristic, direct product factor, Sylow
448C23—22no—
449C23—24no—
450C23—24no—
451C23—24no—
452C23—22no—
453C23—24no—
454C23—24no—
455C23—24no—
456C23—24no—
457C23—24no—
458C23—42no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—42no—
463C23—42no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—41no—
468C23C2×C42×C1114yes—
469C23C23×C4×C1111yescharacteristic
470C23C23×C4×C1112yes—
471C23C11×H(5,𝔽2)12yes—
472C23C11×H(5,𝔽2)12yes—
473C23C11×H(5,𝔽2)12yes—
474C23C11×H(5,𝔽2)11yescharacteristic
475C23C11×H(5,𝔽2)11yescharacteristic
476C23C11×2−1+412yes—
477C23C11×2−1+412yes—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—416no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4C2×C42×C1118yes—
531C22—24no—
532C22—28no—
533C22—44no—
534C22—44no—
535C22—44no—
536C22—42no—
537C22—42no—
538C22—44no—
539C22—44no—
540C22C22×C42×C1111yescharacteristic
541C22C11×#51812yes—
542C22C11×#51812yes—
543C22C11×#51811yescharacteristic
544C22C11×#51812yes—
545C22C11×#51911yescharacteristic
546C22C11×#52012yes—
547C22C11×#52012yes—
548C22C11×#52012yes—
549C22C11×#52012yes—
550C22C11×#52012yes—
551C22C11×#56012yes—
552C22C11×#56011yescharacteristic
553C22C11×#56011yescharacteristic
554C22C11×H(3,𝔽4)11yescharacteristic
555C22C11×#56212yes—
556C22C11×#56212yes—
557C22C11×#56212yes—
558C22C11×#56312yes—
559C22C11×#56312yes—
560C22C11×#56311yescharacteristic
561C4—28no—
562C4—44no—
563C4—44no—
564C4—42no—
565C4—44no—
566C4—42no—
567C4—44no—
568C4—44no—
569C2—44no—
570C2C11×#227411yescharacteristic
571C2C11×#227512yes—
572C2C11×#237511yescharacteristic
573C2C11×#237611yescharacteristic
574C2C11×#237612yes—
575C2C11×#237712yes—
576C2C11×#237812yes—
577C2C11×#237912yes—
578C2C11×#238312yes—
subgroupG/H
center, socleC24×C11C24
commutatorC22C22×C42×C11
Frattini, cosocleC24C24×C11
prime radicalC25×C11C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
5. C11×#1436C2semidirect
6. C11×#1436C2semidirect
7. C11×C4⋊#95C2semidirect
8. C11×#1434C2semidirect
20. C11×#388C4semidirect
21. C11×#385C4semidirect
52. C2×C11×C4⋊C4C2×C4semidirect
70. C2×C42×C11C2×C4semidirect
80. C11×#95C2×C4semidirect
81. C11×#95C2×C4semidirect
82. #13831C11direct (N × H)
155. C11×C22⋊C4C42semidirect
163. #1436C2×C11semidirect
164. #1436C2×C11semidirect
165. C4⋊#95C2×C11semidirect
166. #1434C2×C11semidirect
261. #388C4×C11semidirect
262. #385C4×C11semidirect
331. C2×C4⋊C4C2×C4×C11semidirect
349. C2×C42C2×C4×C11semidirect
359. #95C2×C4×C11semidirect
360. #95C2×C4×C11semidirect
443. C22⋊C4C42×C11semidirect
447. C11#13831direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3882
C2×C11×#3852
C11×#14372
C11×#14362
C11×C4⋊#952
C11×#14342
C11×C22⋊#952
#1383111