Finite Group Databasebeta

← C11×#24132 #14601325

Subgroups — C11×#24132 #14601325

Order 2816.

1336 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#547C211yesmaximal, characteristic
2C2×C11×#477C211yesmaximal, characteristic, complemented
3C2×C11×#440C211yesmaximal, characteristic, complemented
4C11×#2536C211yesmaximal, characteristic, complemented
5C11×#2033C212yesmaximal, complemented
6C11×#2000C212yesmaximal, complemented
7C11×#1993C211yesmaximal, characteristic, complemented
8C11×#1955C211yesmaximal, characteristic, complemented
9C11×#1872C212yesmaximal, complemented
10C11×#1852C212yesmaximal, complemented
11C11×#1804C211yesmaximal, characteristic, complemented
12C22×C11×#41—21no—
13C22×C11×SD16C2211yescharacteristic
14C11×#547—24no—
15C11×#547—24no—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#123—22no—
18C2×C11×C22⋊Q8—21no—
19C2×C11×C22⋊Q8C2212yes—
20C2×C11×#121C2212yes—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C22×C11×C4⋊C4C2212yes—
25C11×#477—24no—
26C11×#440—24no—
27C2×C11×#107C2211yescharacteristic
28C2×C11×#107C2212yes—
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2212yes—
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2212yes—
34C2×C11×C22⋊C8C2212yes—
35C2×C11×C22⋊C8C2212yes—
36C2×C11×#97C2211yescharacteristic
37C11×#398—21no—
38C11×#394—21no—
39C11×#388—22no—
40C11×#382C2211yescharacteristic
41C11×#380C2212yes—
42C11×#340C2212yes—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C2×C11×#41—28no—
46C2×C11×#41—48no—
47C22×Q8×C11—21no—
48C22×Q8×C11C2311yescharacteristic
49C22×D4×C11—22no—
50C22×D4×C11D411yescharacteristic
51C22×D4×C11C2311yescharacteristic
52C23×C4×C11—22no—
53C23×C4×C11—21no—
54C23×C4×C11C2312yes—
55C2×C11×SD16—22no—
56C2×C11×SD16—22no—
57C2×C11×SD16—22no—
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2312yes—
60C22×C8×C11C2311yescharacteristic
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8D414yes—
63C11×#123—216no—
64C11×C22⋊Q8—28no—
65C11×C22⋊Q8—24no—
66C11×C22⋊Q8—42no—
67C11×#121—24no—
68C11×#121—24no—
69C4×Q8×C11—22no—
70C4×Q8×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C4×D4×C11D414yes—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—24no—
78C2×C11×C4⋊C4—24no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4D412yes—
91C2×C42×C11—21no—
92C2×C42×C11C2311yescharacteristic
93C11×#107—22no—
94C11×#107—24no—
95C11×C4⋊C8—22no—
96C11×#103—22no—
97C11×#103—24no—
98C11×#102—22no—
99C11×#102—42no—
100C11×C22⋊C8—24no—
101C11×C22⋊C8—42no—
102C11×#97—22no—
103C11×#95—22no—
104C11×#95—21no—
105C11×#95—21no—
106#24132C1111yesmaximal, characteristic, direct product factor, Sylow
107C24×C11—21no—
108C24×C11C2×D412yes—
109C11×#41—432no—
110C2×Q8×C11—24no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—44no—
117C2×Q8×C11#4112yescomplemented
118C2×D4×C11—24no—
119C2×D4×C11—28no—
120C2×D4×C11—22no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—44no—
127C2×D4×C11—44no—
128C2×D4×C11C2×D412yes—
129C22×C4×C11—28no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11—24no—
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—21no—
142C22×C4×C11—44no—
143C22×C4×C11—44no—
144C22×C4×C11—44no—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C11×SD16—28no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—22no—
153C2×C8×C11—21no—
154C2×C8×C11—22no—
155C2×C8×C11—21no—
156C2×C8×C11—22no—
157C2×C8×C11—21no—
158C2×C8×C11#4112yescomplemented
159C11×C4⋊C4—28no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—44no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4C2×D412yes—
171C11×C4⋊C4C2×D414yes—
172C11×C22⋊C4—28no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—44no—
176C11×C22⋊C4—44no—
177C42×C11—42no—
178C42×C11C2×D412yes—
179C42×C11C2×D412yes—
180C2×#547C2×C1111yescharacteristic
181C2×#477C2×C1111yescharacteristic, complemented
182C2×#440C2×C1111yescharacteristic, complemented
183#2536C2×C1111yescharacteristic, complemented
184#2033C2×C1112yescomplemented
185#2000C2×C1112yescomplemented
186#1993C2×C1111yescharacteristic, complemented
187#1955C2×C1111yescharacteristic, complemented
188#1872C2×C1112yescomplemented
189#1852C2×C1112yescomplemented
190#1804C2×C1111yescharacteristic, complemented
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11AGL(1,ℤ/8)14yes—
203C23×C11C22×D411yescharacteristic
204Q8×C11—22no—
205Q8×C11—22no—
206Q8×C11—48no—
207Q8×C11—41no—
208Q8×C11—41no—
209D4×C11—28no—
210D4×C11—22no—
211D4×C11—22no—
212D4×C11—416no—
213D4×C11—41no—
214D4×C11—41no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—24no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—48no—
224C2×C4×C11—416no—
225C2×C4×C11—41no—
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—41no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11#12012yes—
240C2×C4×C11#12012yes—
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11H(5,𝔽2)11yescharacteristic
246C2×C4×C112−1+411yescharacteristic
247C8×C11—22no—
248C8×C11—41no—
249C8×C11—42no—
250C22×#41—21no—
251C22×SD16C22×C1111yescharacteristic
252#547—24no—
253#547—24no—
254C2×C4⋊Q8C22×C1111yescharacteristic
255C2×#123—22no—
256C2×C22⋊Q8—21no—
257C2×C22⋊Q8C22×C1112yes—
258C2×#121C22×C1112yes—
259C2×C4×Q8C22×C1111yescharacteristic
260C2×C4×D4C22×C1111yescharacteristic
261C2×C4×D4C22×C1111yescharacteristic
262C22×C4⋊C4C22×C1112yes—
263#477—24no—
264#440—24no—
265C2×#107C22×C1112yes—
266C2×#107C22×C1111yescharacteristic
267C2×C4⋊C8C22×C1111yescharacteristic
268C2×#103C22×C1112yes—
269C2×#103C22×C1111yescharacteristic
270C2×#102C22×C1111yescharacteristic
271C2×#102C22×C1112yes—
272C2×C22⋊C8C22×C1112yes—
273C2×C22⋊C8C22×C1112yes—
274C2×#97C22×C1111yescharacteristic
275#398—21no—
276#394—21no—
277#388—22no—
278#382C22×C1111yescharacteristic
279#380C22×C1112yes—
280#340C22×C1112yes—
281#340C22×C1112yes—
282#340C22×C1112yes—
283C22×C11—24no—
284C22×C11—24no—
285C22×C11—24no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—82no—
294C22×C11—82no—
295C22×C11C2×#12011yescharacteristic
296C22×C11#54611yescharacteristic
297C22×C11#54711yescharacteristic
298C22×C11C2×AGL(1,ℤ/8)12yes—
299C22×C11#57812yes—
300C4×C11—22no—
301C4×C11—22no—
302C4×C11—42no—
303C4×C11—42no—
304C4×C11—42no—
305C4×C11—44no—
306C4×C11—81no—
307C4×C11—82no—
308C4×C11#52511yescharacteristic
309C4×C11#53711yescharacteristic
310C4×C11#54811yescharacteristic
311C4×C11#55011yescharacteristic
312C2×#41—28no—
313C2×#41—48no—
314C22×Q8—21no—
315C22×Q8C23×C1111yescharacteristic
316C22×D4—22no—
317C22×D4D4×C1111yescharacteristic
318C22×D4C23×C1111yescharacteristic
319C23×C4—22no—
320C23×C4—21no—
321C23×C4C23×C1112yes—
322C2×SD16—22no—
323C2×SD16—22no—
324C2×SD16—22no—
325C22×C8C23×C1111yescharacteristic
326C22×C8C23×C1112yes—
327C22×C8C23×C1111yescharacteristic
328C4⋊Q8—22no—
329C4⋊Q8D4×C1114yes—
330#123—216no—
331C22⋊Q8—28no—
332C22⋊Q8—24no—
333C22⋊Q8—42no—
334#121—24no—
335#121—24no—
336C4×Q8—22no—
337C4×Q8—22no—
338C4×D4—22no—
339C4×D4—22no—
340C4×D4—22no—
341C4×D4D4×C1114yes—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4D4×C1111yescharacteristic
349C2×C4⋊C4C23×C1111yescharacteristic
350C2×C4⋊C4C23×C1112yes—
351C2×C4⋊C4C23×C1111yescharacteristic
352C2×C4⋊C4C23×C1112yes—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4D4×C1112yes—
358C2×C42—21no—
359C2×C42C23×C1111yescharacteristic
360#107—22no—
361#107—24no—
362C4⋊C8—22no—
363#103—22no—
364#103—24no—
365#102—22no—
366#102—42no—
367C22⋊C8—24no—
368C22⋊C8—42no—
369#97—22no—
370#95—22no—
371#95—21no—
372#95—21no—
373C2×C11—44no—
374C2×C11—82no—
375C2×C11#240711yescharacteristic
376C2×C11#300311yescharacteristic
377C2×C11#301111yescharacteristic
378C2×C11#330812yes—
379C2×C11#334312yes—
380C24—21no—
381C24C2×D4×C1112yes—
382#41—432no—
383C2×Q8—24no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—44no—
390C2×Q8C11×#4112yescomplemented
391C2×D4—24no—
392C2×D4—28no—
393C2×D4—22no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—44no—
400C2×D4—44no—
401C2×D4C2×D4×C1112yes—
402C22×C4—28no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—24no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—44no—
416C22×C4—44no—
417C22×C4—44no—
418C22×C4C2×D4×C1112yes—
419C22×C4C2×D4×C1111yescharacteristic
420C22×C4C2×D4×C1111yescharacteristic
421C22×C4C24×C1111yescharacteristic
422SD16—28no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—22no—
427C2×C8—22no—
428C2×C8—21no—
429C2×C8—22no—
430C2×C8—21no—
431C2×C8C11×#4112yescomplemented
432C4⋊C4—28no—
433C4⋊C4—24no—
434C4⋊C4—22no—
435C4⋊C4—21no—
436C4⋊C4—22no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—44no—
442C4⋊C4—42no—
443C4⋊C4C2×D4×C1112yes—
444C4⋊C4C2×D4×C1114yes—
445C22⋊C4—28no—
446C22⋊C4—24no—
447C22⋊C4—24no—
448C22⋊C4—44no—
449C22⋊C4—44no—
450C42—42no—
451C42C2×D4×C1112yes—
452C42C2×D4×C1112yes—
453C11#2413211yescharacteristic, direct product factor, Sylow
454C23—22no—
455C23—22no—
456C23—22no—
457C23—22no—
458C23—22no—
459C23—22no—
460C23—22no—
461C23—41no—
462C23—41no—
463C23—42no—
464C23—42no—
465C23C11×AGL(1,ℤ/8)14yes—
466C23C22×D4×C1111yescharacteristic
467Q8—22no—
468Q8—22no—
469Q8—48no—
470Q8—41no—
471Q8—41no—
472D4—28no—
473D4—22no—
474D4—22no—
475D4—416no—
476D4—41no—
477D4—41no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—48no—
487C2×C4—416no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4C11×#12012yes—
503C2×C4C11×#12012yes—
504C2×C4C22×D4×C1111yescharacteristic
505C2×C4C22×D4×C1111yescharacteristic
506C2×C4C2×C11×#4111yescharacteristic
507C2×C4C2×C11×#4111yescharacteristic
508C2×C4C11×H(5,𝔽2)11yescharacteristic
509C2×C4C11×2−1+411yescharacteristic
510C8—22no—
511C8—41no—
512C8—42no—
513C22—24no—
514C22—24no—
515C22—24no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—42no—
523C22—82no—
524C22—82no—
525C22C2×C11×#12011yescharacteristic
526C22C11×#54611yescharacteristic
527C22C11×#54711yescharacteristic
528C22C2×C11×AGL(1,ℤ/8)12yes—
529C22C11×#57812yes—
530C4—22no—
531C4—22no—
532C4—42no—
533C4—42no—
534C4—42no—
535C4—44no—
536C4—81no—
537C4—82no—
538C4C11×#52511yescharacteristic
539C4C11×#53711yescharacteristic
540C4C11×#54811yescharacteristic
541C4C11×#55011yescharacteristic
542C2—44no—
543C2—82no—
544C2C11×#240711yescharacteristic
545C2C11×#300311yescharacteristic
546C2C11×#301111yescharacteristic
547C2C11×#330812yes—
548C2C11×#334312yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#547C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#477C2semidirect
3. C2×C11×#440C2semidirect
4. C11×#2536C2semidirect
5. C11×#2033C2semidirect
6. C11×#2000C2semidirect
7. C11×#1993C2semidirect
8. C11×#1955C2semidirect
9. C11×#1872C2semidirect
10. C11×#1852C2semidirect
11. C11×#1804C2semidirect
106. #24132C11direct (N × H)
117. C2×Q8×C11#41semidirect
158. C2×C8×C11#41semidirect
181. C2×#477C2×C11semidirect
182. C2×#440C2×C11semidirect
183. #2536C2×C11semidirect
184. #2033C2×C11semidirect
185. #2000C2×C11semidirect
186. #1993C2×C11semidirect
187. #1955C2×C11semidirect
188. #1872C2×C11semidirect
189. #1852C2×C11semidirect
190. #1804C2×C11semidirect
390. C2×Q8C11×#41semidirect
431. C2×C8C11×#41semidirect
453. C11#24132direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5472
C2×C11×#4772
C2×C11×#4402
C11×#25362
C11×#20332
C11×#20002
C11×#19932
C11×#19552
C11×#18722
C11×#18522
C11×#18042
#2413211