Finite Group Databasebeta

← C11×#24305 #14601498

Subgroups — C11×#24305 #14601498

Order 2816.

1162 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#125C211yesmaximal, characteristic, complemented
2C2×C11×#478C212yesmaximal, complemented
3C4×C11×#121C211yesmaximal, characteristic
4C11×#2059C212yesmaximal, complemented
5C11×#2025C212yesmaximal, complemented
6C11×#1989C212yesmaximal, complemented
7C11×#1874C211yesmaximal, characteristic
8C11×#1874C211yesmaximal, characteristic
9C11×#1853C211yesmaximal, characteristic, complemented
10C11×#1852C211yesmaximal, characteristic, complemented
11C11×#1797C211yesmaximal, characteristic, complemented
12C2×C11×#125—28no—
13C2×C11×#125—21no—
14C2×C11×#125—21no—
15C2×C11×#125C2212yes—
16C2×C11×#125C2212yes—
17C2×C11×#121C2211yescharacteristic
18C2×C4×D4×C11—21no—
19C2×C4×D4×C11C2211yescharacteristic
20C22×C11×C4⋊C4—21no—
21C22×C11×C4⋊C4—21no—
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C42×C11C2211yescharacteristic
25C11×#478—28no—
26C2×C11×#107C2212yes—
27C2×C11×#106C2212yes—
28C2×C11×C4⋊C8C2212yes—
29C2×C11×#102C2212yes—
30C2×C11×#102C2212yes—
31C2×C11×C22⋊C8C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic
33C11×#390C2211yescharacteristic
34C11×#389C2211yescharacteristic
35C11×#388—21no—
36C11×#386—21no—
37C11×#380C2211yescharacteristic
38C4×C11×C4⋊C4C2211yescharacteristic
39C4×C11×C22⋊C4—21no—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#340C2212yes—
44C11×#336C2212yes—
45C22×D4×C11—21no—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11—21no—
49C23×C4×C11—21no—
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D411yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C22×C8×C11C2312yes—
54C22×C8×C11C2312yes—
55C11×#125—28no—
56C11×#125—28no—
57C11×#125—24no—
58C11×#125—24no—
59C11×#125—24no—
60C11×#125D418yescomplemented
61C11×#121—22no—
62C11×#121Q814yes—
63C4×D4×C11—24no—
64C4×D4×C11—44no—
65C2×C11×C4⋊C4—28no—
66C2×C11×C4⋊C4—28no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—24no—
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C42×C11—24no—
87C2×C42×C11—21no—
88C2×C42×C11D411yescharacteristic
89C2×C42×C11D411yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C11×#107—24no—
93C11×#106—24no—
94C11×C4⋊C8—24no—
95C11×#102—24no—
96C11×#102—24no—
97C11×C22⋊C8—22no—
98C11×C22⋊C8—22no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102#24305C1111yesmaximal, characteristic, direct product factor, Sylow
103C24×C11—21no—
104C24×C11C2×D411yescharacteristic
105C2×D4×C11—24no—
106C2×D4×C11—22no—
107C2×D4×C11—21no—
108C2×D4×C11—22no—
109C2×D4×C11—42no—
110C2×D4×C11—42no—
111C2×D4×C11C2×Q812yes—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—24no—
115C22×C4×C11—24no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—41no—
126C22×C4×C11—41no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×Q812yes—
140C22×C4×C11#4112yes—
141C22×C4×C11C2411yescharacteristic
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—28no—
151C11×C4⋊C4—28no—
152C11×C4⋊C4—28no—
153C11×C4⋊C4—28no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—42no—
160C11×C4⋊C4C2×D414yes—
161C11×C4⋊C4C2×D414yes—
162C11×C4⋊C4C2×Q812yes—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—42no—
165C11×C22⋊C4—42no—
166C11×C22⋊C4—42no—
167C11×C22⋊C4—42no—
168C42×C11—22no—
169C42×C11—22no—
170C42×C11—22no—
171C42×C11—42no—
172C42×C11C2×D414yes—
173C22×#125C2×C1111yescharacteristic, complemented
174C2×#478C2×C1112yescomplemented
175C4×#121C2×C1111yescharacteristic
176#2059C2×C1112yescomplemented
177#2025C2×C1112yescomplemented
178#1989C2×C1112yescomplemented
179#1874C2×C1111yescharacteristic
180#1874C2×C1111yescharacteristic
181#1853C2×C1111yescharacteristic, complemented
182#1852C2×C1111yescharacteristic, complemented
183#1797C2×C1111yescharacteristic, complemented
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—22no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11C22⋊Q812yes—
196C23×C11#13512yes—
197C23×C11AGL(1,ℤ/8)12yes—
198C23×C11C22×D411yescharacteristic
199D4×C11—24no—
200D4×C11—48no—
201D4×C11—42no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—44no—
220C2×C4×C11—44no—
221C2×C4×C11—48no—
222C2×C4×C11—48no—
223C2×C4×C11—42no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—84no—
236C2×C4×C11#12012yes—
237C2×C4×C11#12012yes—
238C2×C4×C11C22⋊Q812yes—
239C2×C4×C11C22×D412yes—
240C2×C4×C11C22×Q811yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C112−1+412yes—
243C8×C11—42no—
244C8×C11—42no—
245C2×#125—28no—
246C2×#125—21no—
247C2×#125—21no—
248C2×#125C22×C1112yes—
249C2×#125C22×C1112yes—
250C2×#121C22×C1111yescharacteristic
251C2×C4×D4—21no—
252C2×C4×D4C22×C1111yescharacteristic
253C22×C4⋊C4—21no—
254C22×C4⋊C4—21no—
255C22×C4⋊C4C22×C1111yescharacteristic
256C22×C4⋊C4C22×C1111yescharacteristic
257C22×C42C22×C1111yescharacteristic
258#478—28no—
259C2×#107C22×C1112yes—
260C2×#106C22×C1112yes—
261C2×C4⋊C8C22×C1112yes—
262C2×#102C22×C1112yes—
263C2×#102C22×C1112yes—
264C2×C22⋊C8C22×C1111yescharacteristic
265C2×C22⋊C8C22×C1111yescharacteristic
266#390C22×C1111yescharacteristic
267#389C22×C1111yescharacteristic
268#388—21no—
269#386—21no—
270#380C22×C1111yescharacteristic
271C4×C4⋊C4C22×C1111yescharacteristic
272C4×C22⋊C4—21no—
273#340C22×C1112yes—
274#340C22×C1112yes—
275#340C22×C1112yes—
276#340C22×C1112yes—
277#336C22×C1112yes—
278C22×C11—22no—
279C22×C11—22no—
280C22×C11—22no—
281C22×C11—22no—
282C22×C11—22no—
283C22×C11—22no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—81no—
288C22×C11—81no—
289C22×C11—81no—
290C22×C11—81no—
291C22×C11#47814yescomplemented
292C22×C11C2×#12011yescharacteristic
293C22×C11C2×C22⋊Q811yescharacteristic
294C22×C11#53611yescharacteristic
295C22×C11C2×#13511yescharacteristic
296C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
297C22×C11#57511yescharacteristic
298C22×C11#57511yescharacteristic
299C4×C11—22no—
300C4×C11—22no—
301C4×C11—22no—
302C4×C11—42no—
303C4×C11—41no—
304C4×C11—44no—
305C4×C11—41no—
306C4×C11—44no—
307C4×C11—81no—
308C4×C11—81no—
309C4×C11#54812yes—
310C4×C11D4×Q812yes—
311C22×D4—21no—
312C22×D4C23×C1111yescharacteristic
313C23×C4—21no—
314C23×C4—21no—
315C23×C4—21no—
316C23×C4D4×C1111yescharacteristic
317C23×C4D4×C1111yescharacteristic
318C23×C4C23×C1111yescharacteristic
319C22×C8C23×C1112yes—
320C22×C8C23×C1112yes—
321#125—28no—
322#125—28no—
323#125—24no—
324#125—24no—
325#125—24no—
326#125D4×C1118yescomplemented
327#121—22no—
328#121Q8×C1114yes—
329C4×D4—24no—
330C4×D4—44no—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—28no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4C23×C1111yescharacteristic
343C2×C4⋊C4C23×C1111yescharacteristic
344C2×C4⋊C4C23×C1112yes—
345C2×C4⋊C4C23×C1112yes—
346C2×C4⋊C4C23×C1111yescharacteristic
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C42—24no—
353C2×C42—21no—
354C2×C42D4×C1111yescharacteristic
355C2×C42D4×C1111yescharacteristic
356C2×C42C23×C1111yescharacteristic
357C2×C42C23×C1111yescharacteristic
358#107—24no—
359#106—24no—
360C4⋊C8—24no—
361#102—24no—
362#102—24no—
363C22⋊C8—22no—
364C22⋊C8—22no—
365#95—21no—
366#95—21no—
367#95—21no—
368C2×C11—24no—
369C2×C11—82no—
370C2×C11#240911yescharacteristic
371C2×C11#300211yescharacteristic
372C2×C11#300611yescharacteristic
373C2×C11C2×#47811yescharacteristic
374C2×C11#308011yescharacteristic
375C2×C11#323211yescharacteristic
376C2×C11#323411yescharacteristic
377C24—21no—
378C24C2×D4×C1111yescharacteristic
379C2×D4—24no—
380C2×D4—22no—
381C2×D4—21no—
382C2×D4—22no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4C2×Q8×C1112yes—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—42no—
407C22×C4—42no—
408C22×C4C2×D4×C1111yescharacteristic
409C22×C4C2×D4×C1111yescharacteristic
410C22×C4C2×D4×C1111yescharacteristic
411C22×C4C2×D4×C1111yescharacteristic
412C22×C4C2×D4×C1111yescharacteristic
413C22×C4C2×Q8×C1112yes—
414C22×C4C11×#4112yes—
415C22×C4C24×C1111yescharacteristic
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8—22no—
422C4⋊C4—24no—
423C4⋊C4—24no—
424C4⋊C4—28no—
425C4⋊C4—28no—
426C4⋊C4—28no—
427C4⋊C4—28no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—21no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—42no—
434C4⋊C4C2×D4×C1114yes—
435C4⋊C4C2×D4×C1114yes—
436C4⋊C4C2×Q8×C1112yes—
437C22⋊C4—24no—
438C22⋊C4—42no—
439C22⋊C4—42no—
440C22⋊C4—42no—
441C22⋊C4—42no—
442C42—22no—
443C42—22no—
444C42—22no—
445C42—42no—
446C42C2×D4×C1114yes—
447C11#2430511yescharacteristic, direct product factor, Sylow
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—22no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23—41no—
458C23—41no—
459C23C11×C22⋊Q812yes—
460C23C11×#13512yes—
461C23C11×AGL(1,ℤ/8)12yes—
462C23C22×D4×C1111yescharacteristic
463D4—24no—
464D4—48no—
465D4—42no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—44no—
484C2×C4—44no—
485C2×C4—48no—
486C2×C4—48no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—84no—
500C2×C4C11×#12012yes—
501C2×C4C11×#12012yes—
502C2×C4C11×C22⋊Q812yes—
503C2×C4C22×D4×C1112yes—
504C2×C4C22×Q8×C1111yescharacteristic
505C2×C4C2×C11×#4111yescharacteristic
506C2×C4C11×2−1+412yes—
507C8—42no—
508C8—42no—
509C22—22no—
510C22—22no—
511C22—22no—
512C22—22no—
513C22—22no—
514C22—22no—
515C22—42no—
516C22—42no—
517C22—42no—
518C22—81no—
519C22—81no—
520C22—81no—
521C22—81no—
522C22C11×#47814yescomplemented
523C22C2×C11×#12011yescharacteristic
524C22C2×C11×C22⋊Q811yescharacteristic
525C22C11×#53611yescharacteristic
526C22C2×C11×#13511yescharacteristic
527C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
528C22C11×#57511yescharacteristic
529C22C11×#57511yescharacteristic
530C4—22no—
531C4—22no—
532C4—22no—
533C4—41no—
534C4—44no—
535C4—41no—
536C4—44no—
537C4—42no—
538C4—81no—
539C4—81no—
540C4C11×#54812yes—
541C4D4×Q8×C1112yes—
542C2—24no—
543C2—82no—
544C2C11×#240911yescharacteristic
545C2C11×#300211yescharacteristic
546C2C11×#300611yescharacteristic
547C2C2×C11×#47811yescharacteristic
548C2C11×#308011yescharacteristic
549C2C11×#323211yescharacteristic
550C2C11×#323411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#125C2semidirect
2. C2×C11×#478C2semidirect
4. C11×#2059C2semidirect
5. C11×#2025C2semidirect
6. C11×#1989C2semidirect
9. C11×#1853C2semidirect
10. C11×#1852C2semidirect
11. C11×#1797C2semidirect
60. C11×#125D4semidirect
102. #24305C11direct (N × H)
173. C22×#125C2×C11semidirect
174. C2×#478C2×C11semidirect
176. #2059C2×C11semidirect
177. #2025C2×C11semidirect
178. #1989C2×C11semidirect
181. #1853C2×C11semidirect
182. #1852C2×C11semidirect
183. #1797C2×C11semidirect
291. C22×C11#478semidirect
326. #125D4×C11semidirect
447. C11#24305direct (N × H)
522. C22C11×#478semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#1252
C2×C11×#4782
C4×C11×#1212
C11×#20592
C11×#20252
C11×#19892
C11×#18742
C11×#18532
C11×#18522
C11×#17972
#2430511