Finite Group Databasebeta

← C11×#14649 #14591842

Subgroups — C11×#14649 #14591842

Order 2816.

1290 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#393C211yesmaximal, characteristic
2C11×#1446C212yesmaximal, complemented
3C11×#1443C212yesmaximal, complemented
4C11×#1442C212yesmaximal, complemented
5C11×#1440C212yesmaximal
6C11×#1440C211yesmaximal, characteristic
7C11×#1439C212yesmaximal
8C11×#1437C211yesmaximal, characteristic
9C11×#1436C212yesmaximal, complemented
10C23×Q8×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2212yes—
12C22×C11×C22⋊C4C2212yes—
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2212yes—
17C22×C42×C11C2211yescharacteristic
18C11×#393C418yescomplemented
19C2×C11×#95C2212yes—
20C2×C11×#95C2212yes—
21C2×C11×#95C2212yes—
22C2×C11×#95C2212yes—
23C2×C11×#95C2212yes—
24C2×C11×#95C2211yescharacteristic
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27C2×C11×#95C2212yes—
28C2×C11×#95C2212yes—
29C2×C11×#95C2212yes—
30C2×C11×#95C2212yes—
31C2×C11×#95C2211yescharacteristic
32C25×C11C2311yescharacteristic
33C22×Q8×C11—42no—
34C22×Q8×C11—41no—
35C22×Q8×C11—42no—
36C22×Q8×C11—41no—
37C22×Q8×C11C2×C414yes—
38C23×C4×C11C2312yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2312yes—
45C23×C4×C11C2312yes—
46C2×C11×C4⋊C4—24no—
47C2×C11×C4⋊C4—42no—
48C2×C11×C4⋊C4—42no—
49C2×C11×C22⋊C4—24no—
50C2×C11×C22⋊C4—41no—
51C2×C11×C22⋊C4—42no—
52C2×C11×C22⋊C4—41no—
53C2×C11×C22⋊C4—42no—
54C2×C11×C22⋊C4—42no—
55C2×C11×C22⋊C4—42no—
56C2×C11×C22⋊C4—41no—
57C2×C11×C22⋊C4—42no—
58C2×C11×C22⋊C4—41no—
59C2×C11×C22⋊C4—42no—
60C2×C11×C22⋊C4C2×C414yes—
61C2×C11×C22⋊C4C2×C418yes—
62C2×C42×C11—41no—
63C2×C42×C11—42no—
64C11×#95—24no—
65C11×#95—42no—
66C11×#95—42no—
67C11×#95—42no—
68C11×#95—41no—
69C11×#95—42no—
70C11×#95—42no—
71C11×#95—42no—
72C11×#95—42no—
73C11×#95—42no—
74C11×#95—42no—
75C11×#95C2×C418yes—
76C11×#95C2×C414yes—
77#14649C1111yesmaximal, characteristic, direct product factor, Sylow
78C24×C11—22no—
79C24×C11—22no—
80C24×C11—22no—
81C24×C11—21no—
82C24×C11—21no—
83C24×C11—22no—
84C24×C11—22no—
85C24×C11—22no—
86C24×C11C22×C412yes—
87C24×C11C2411yescharacteristic
88C2×Q8×C11—44no—
89C2×Q8×C11—48no—
90C2×Q8×C11—48no—
91C2×Q8×C11—44no—
92C2×Q8×C11—44no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—21no—
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—22no—
107C22×C4×C11—22no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
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—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—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11C22×C414yes—
141C22×C4×C11C22×C412yes—
142C22×C4×C11C22×C412yes—
143C22×C4×C11C22×C414yes—
144C22×C4×C11#4114yes—
145C11×C4⋊C4—48no—
146C11×C22⋊C4—48no—
147C11×C22⋊C4—44no—
148C11×C22⋊C4—48no—
149C11×C22⋊C4—44no—
150C11×C22⋊C4—44no—
151C42×C11—44no—
152C2×#393C2×C1111yescharacteristic
153#1446C2×C1112yescomplemented
154#1443C2×C1112yescomplemented
155#1442C2×C1112yescomplemented
156#1440C2×C1112yes—
157#1440C2×C1111yescharacteristic
158#1439C2×C1112yes—
159#1437C2×C1111yescharacteristic
160#1436C2×C1112yescomplemented
161C23×C11—22no—
162C23×C11—22no—
163C23×C11—24no—
164C23×C11—22no—
165C23×C11—24no—
166C23×C11—42no—
167C23×C11—42no—
168C23×C11—42no—
169C23×C11—42no—
170C23×C11—42no—
171C23×C11—42no—
172C23×C11—42no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—41no—
182C23×C11C23×C411yescharacteristic
183C23×C11C2×#4112yes—
184C23×C11H(5,𝔽2)12yes—
185C23×C11H(5,𝔽2)12yes—
186C23×C11H(5,𝔽2)11yescharacteristic
187C23×C11H(5,𝔽2)11yescharacteristic
188C23×C11H(5,𝔽2)12yes—
189C23×C112−1+412yes—
190C23×C112−1+412yes—
191Q8×C11—416no—
192C2×C4×C11—24no—
193C2×C4×C11—24no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—24no—
197C2×C4×C11—24no—
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—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—41no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
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—42no—
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—
244C23×Q8C22×C1111yescharacteristic
245C22×C4⋊C4C22×C1112yes—
246C22×C22⋊C4C22×C1112yes—
247C22×C22⋊C4C22×C1111yescharacteristic
248C22×C22⋊C4C22×C1111yescharacteristic
249C22×C22⋊C4C22×C1111yescharacteristic
250C22×C22⋊C4C22×C1112yes—
251C22×C42C22×C1111yescharacteristic
252#393C4×C1118yescomplemented
253C2×#95C22×C1112yes—
254C2×#95C22×C1112yes—
255C2×#95C22×C1112yes—
256C2×#95C22×C1112yes—
257C2×#95C22×C1112yes—
258C2×#95C22×C1111yescharacteristic
259C2×#95C22×C1112yes—
260C2×#95C22×C1112yes—
261C2×#95C22×C1112yes—
262C2×#95C22×C1112yes—
263C2×#95C22×C1112yes—
264C2×#95C22×C1112yes—
265C2×#95C22×C1111yescharacteristic
266C22×C11—42no—
267C22×C11—44no—
268C22×C11—42no—
269C22×C11—44no—
270C22×C11—42no—
271C22×C11—82no—
272C22×C11—82no—
273C22×C11—82no—
274C22×C11—82no—
275C22×C11C4×#4111yescharacteristic
276C22×C11#51811yescharacteristic
277C22×C11#51812yes—
278C22×C11#51911yescharacteristic
279C22×C11#52012yes—
280C22×C11#53812yes—
281C22×C11#53812yes—
282C22×C11#53912yes—
283C22×C11#54212yes—
284C22×C11#54212yes—
285C22×C11#54212yes—
286C22×C11#56012yes—
287C22×C11#56011yescharacteristic
288C22×C11H(3,𝔽4)11yescharacteristic
289C22×C11H(3,𝔽4)11yescharacteristic
290C22×C11#56212yes—
291C22×C11#56212yes—
292C22×C11#56212yes—
293C22×C11#56312yes—
294C22×C11#56312yes—
295C22×C11#56311yescharacteristic
296C4×C11—44no—
297C4×C11—44no—
298C4×C11—42no—
299C4×C11—44no—
300C4×C11—42no—
301C4×C11—82no—
302C4×C11—82no—
303C4×C11—82no—
304C25C23×C1111yescharacteristic
305C22×Q8—42no—
306C22×Q8—41no—
307C22×Q8—42no—
308C22×Q8—41no—
309C22×Q8C2×C4×C1114yes—
310C23×C4C23×C1112yes—
311C23×C4C23×C1112yes—
312C23×C4C23×C1112yes—
313C23×C4C23×C1112yes—
314C23×C4C23×C1111yescharacteristic
315C23×C4C23×C1112yes—
316C23×C4C23×C1111yescharacteristic
317C23×C4C23×C1112yes—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—41no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—41no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—41no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—41no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4C2×C4×C1114yes—
333C2×C22⋊C4C2×C4×C1118yes—
334C2×C42—41no—
335C2×C42—42no—
336#95—24no—
337#95—42no—
338#95—42no—
339#95—42no—
340#95—41no—
341#95—42no—
342#95—42no—
343#95—42no—
344#95—42no—
345#95—42no—
346#95—42no—
347#95C2×C4×C1118yes—
348#95C2×C4×C1114yes—
349C2×C11—82no—
350C2×C11#233211yescharacteristic
351C2×C11#233712yes—
352C2×C11#237511yescharacteristic
353C2×C11#237812yes—
354C2×C11#237911yescharacteristic
355C2×C11#282412yes—
356C2×C11#283012yes—
357C2×C11#283212yes—
358C2×C11#283812yes—
359C24—22no—
360C24—22no—
361C24—22no—
362C24—21no—
363C24—21no—
364C24—22no—
365C24—22no—
366C24—22no—
367C24C22×C4×C1112yes—
368C24C24×C1111yescharacteristic
369C2×Q8—48no—
370C2×Q8—44no—
371C2×Q8—48no—
372C2×Q8—44no—
373C2×Q8—44no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—22no—
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—21no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—22no—
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—22no—
408C22×C4—22no—
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×C4C22×C4×C1114yes—
422C22×C4C22×C4×C1112yes—
423C22×C4C22×C4×C1114yes—
424C22×C4C22×C4×C1112yes—
425C22×C4C11×#4114yes—
426C4⋊C4—48no—
427C22⋊C4—44no—
428C22⋊C4—48no—
429C22⋊C4—48no—
430C22⋊C4—44no—
431C22⋊C4—44no—
432C42—44no—
433C11#1464911yescharacteristic, direct product factor, Sylow
434C23—22no—
435C23—24no—
436C23—22no—
437C23—22no—
438C23—24no—
439C23—42no—
440C23—42no—
441C23—42no—
442C23—42no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—41no—
447C23—41no—
448C23—41no—
449C23—42no—
450C23—42no—
451C23—42no—
452C23—42no—
453C23—42no—
454C23—41no—
455C23C23×C4×C1111yescharacteristic
456C23C2×C11×#4112yes—
457C23C11×H(5,𝔽2)12yes—
458C23C11×H(5,𝔽2)12yes—
459C23C11×H(5,𝔽2)11yescharacteristic
460C23C11×H(5,𝔽2)11yescharacteristic
461C23C11×H(5,𝔽2)12yes—
462C23C11×2−1+412yes—
463C23C11×2−1+412yes—
464Q8—416no—
465C2×C4—24no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
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—42no—
517C22—44no—
518C22—42no—
519C22—42no—
520C22—44no—
521C22—42no—
522C22—82no—
523C22—82no—
524C22—82no—
525C22—82no—
526C22C4×C11×#4111yescharacteristic
527C22C11×#51812yes—
528C22C11×#51811yescharacteristic
529C22C11×#51911yescharacteristic
530C22C11×#52012yes—
531C22C11×#53812yes—
532C22C11×#53812yes—
533C22C11×#53912yes—
534C22C11×#54212yes—
535C22C11×#54212yes—
536C22C11×#54212yes—
537C22C11×#56012yes—
538C22C11×#56011yescharacteristic
539C22C11×H(3,𝔽4)11yescharacteristic
540C22C11×H(3,𝔽4)11yescharacteristic
541C22C11×#56212yes—
542C22C11×#56212yes—
543C22C11×#56212yes—
544C22C11×#56312yes—
545C22C11×#56312yes—
546C22C11×#56311yescharacteristic
547C4—42no—
548C4—44no—
549C4—44no—
550C4—44no—
551C4—42no—
552C4—82no—
553C4—82no—
554C4—82no—
555C2—82no—
556C2C11×#233211yescharacteristic
557C2C11×#233712yes—
558C2C11×#237511yescharacteristic
559C2C11×#237812yes—
560C2C11×#237911yescharacteristic
561C2C11×#282412yes—
562C2C11×#283012yes—
563C2C11×#283212yes—
564C2C11×#283812yes—
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. C11×#1446C2semidirect
3. C11×#1443C2semidirect
4. C11×#1442C2semidirect
9. C11×#1436C2semidirect
18. C11×#393C4semidirect
77. #14649C11direct (N × H)
153. #1446C2×C11semidirect
154. #1443C2×C11semidirect
155. #1442C2×C11semidirect
160. #1436C2×C11semidirect
252. #393C4×C11semidirect
433. C11#14649direct (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
C11×#14462
C11×#14432
C11×#14422
C11×#14402
C11×#14392
C11×#14372
C11×#14362
#1464911