Finite Group Databasebeta

← C11×#24478 #14601671

Subgroups — C11×#24478 #14601671

Order 2816.

1232 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
1C2×C11×#481C211yesmaximal, characteristic, complemented
2C22×C11×#102C211yesmaximal, characteristic, complemented
3C11×#2433C211yesmaximal, characteristic
4C11×#2345C211yesmaximal, characteristic, complemented
5C11×#2065C212yesmaximal, complemented
6C11×#2041C212yesmaximal, complemented
7C11×#1982C212yesmaximal, complemented
8C11×#1926C212yesmaximal, complemented
9C11×#1893C211yesmaximal, characteristic, complemented
10C11×#1850C211yesmaximal, characteristic, complemented
11C11×#1786C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×#127C2212yes—
15C2×C11×#121C2211yescharacteristic
16C2×C11×#120—21no—
17C2×C11×#120—21no—
18C22×C11×C4⋊C4C2211yescharacteristic
19C11×#481—24no—
20C2×C11×#106C2211yescharacteristic, complemented
21C2×C11×#106C2211yescharacteristic, complemented
22C2×C11×C4⋊C8C2212yescomplemented
23C2×C11×#102—24no—
24C2×C11×#102C2212yes—
25C2×C11×#102C2212yes—
26C2×C11×#102C2212yes—
27C2×C11×#102C2212yes—
28C2×C11×#102C2211yescharacteristic, complemented
29C2×C11×#102C2211yescharacteristic, complemented
30C2×C11×#102C2212yescomplemented
31C2×C11×C22⋊C8C2211yescharacteristic
32C11×#392—22no—
33C11×#390C2212yes—
34C11×#389C2212yescomplemented
35C11×#387—22no—
36C11×#380—21no—
37C11×#380C2211yescharacteristic
38C4×C11×C4⋊C4C2212yescomplemented
39C4×C11×C22⋊C4—21no—
40C4×C11×C22⋊C4C2211yescharacteristic
41C11×#340C2212yescomplemented
42C11×#336C2212yescomplemented
43C25×C11—21no—
44C22×D4×C11—24no—
45C22×D4×C11—21no—
46C22×D4×C11—22no—
47C22×D4×C11—21no—
48C22×D4×C11—22no—
49C22×D4×C11—22no—
50C22×D4×C11—22no—
51C22×D4×C11—42no—
52C22×D4×C11C2311yescharacteristic
53C22×D4×C11C2312yes—
54C23×C4×C11—21no—
55C23×C4×C11C2311yescharacteristic
56C22×C8×C11—22no—
57C22×C8×C11—42no—
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2312yes—
60C22×C8×C11C2311yescharacteristic
61C11×#127—24no—
62C11×#127—42no—
63C11×#121—22no—
64C11×#121—22no—
65C11×#120—44no—
66C11×#120—44no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4D414yescomplemented
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4D411yescharacteristic
80C2×C11×C22⋊C4D411yescharacteristic
81C2×C42×C11—22no—
82C2×C42×C11C2312yes—
83C11×#106—22no—
84C11×#106—22no—
85C11×C4⋊C8—42no—
86C11×#102—24no—
87C11×#102—24no—
88C11×#102—24no—
89C11×#102—22no—
90C11×#102—22no—
91C11×#102—42no—
92C11×#102—42no—
93C11×C22⋊C8—22no—
94C11×#95—22no—
95C11×#95—22no—
96C11×#95—21no—
97C11×#95D412yes—
98#24478C1111yesmaximal, characteristic, direct product factor, Sylow
99C24×C11—22no—
100C24×C11—21no—
101C24×C11—44no—
102C24×C11—42no—
103C24×C11—42no—
104C24×C11—42no—
105C24×C11—82no—
106C24×C11C2×D411yescharacteristic
107C2×D4×C11—28no—
108C2×D4×C11—22no—
109C2×D4×C11—21no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—21no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—48no—
118C2×D4×C11—44no—
119C2×D4×C11—44no—
120C2×D4×C11—44no—
121C2×D4×C11—44no—
122C2×D4×C11—44no—
123C2×D4×C11—42no—
124C2×D4×C11—42no—
125C2×D4×C11—42no—
126C2×D4×C11—42no—
127C2×D4×C11—44no—
128C2×D4×C11—82no—
129C2×D4×C11—82no—
130C2×D4×C11#4114yes—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—24no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—82no—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D412yes—
143C22×C4×C11#4112yes—
144C22×C4×C11C2411yescharacteristic
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—44no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—82no—
161C11×C4⋊C4C2×D412yes—
162C11×C4⋊C4C2×D412yes—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—44no—
165C11×C22⋊C4—42no—
166C11×C22⋊C4—42no—
167C11×C22⋊C4—44no—
168C11×C22⋊C4SD1614yes—
169C42×C11—22no—
170C42×C11—22no—
171C42×C11—82no—
172C2×#481C2×C1111yescharacteristic, complemented
173C22×#102C2×C1111yescharacteristic, complemented
174#2433C2×C1111yescharacteristic
175#2345C2×C1111yescharacteristic, complemented
176#2065C2×C1112yescomplemented
177#2041C2×C1112yescomplemented
178#1982C2×C1112yescomplemented
179#1926C2×C1112yescomplemented
180#1893C2×C1111yescharacteristic, complemented
181#1850C2×C1111yescharacteristic, complemented
182#1786C2×C1111yescharacteristic, complemented
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—24no—
186C23×C11—48no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—41no—
194C23×C11—42no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—42no—
198C23×C11—88no—
199C23×C11—88no—
200C23×C11—84no—
201C23×C11—84no—
202C23×C11#12112yes—
203C23×C11C2×SD1612yes—
204C23×C11AGL(1,ℤ/8)12yes—
205C23×C11C22×D411yescharacteristic
206D4×C11—24no—
207D4×C11—24no—
208D4×C11—48no—
209D4×C11—41no—
210D4×C11—42no—
211D4×C11—41no—
212D4×C11—42no—
213D4×C11—42no—
214D4×C11—88no—
215D4×C11—88no—
216D4×C11—84no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—41no—
231C2×C4×C11—42no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—84no—
237C2×C4×C11#12112yes—
238C2×C4×C11C2×SD1614yes—
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C2×#4112yes—
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11H(5,𝔽2)12yes—
243C8×C11—41no—
244C8×C11—41no—
245C8×C11—42no—
246C23×D4C22×C1111yescharacteristic
247C23×C8C22×C1111yescharacteristic
248C2×#127C22×C1112yes—
249C2×#121C22×C1111yescharacteristic
250C2×#120—21no—
251C2×#120—21no—
252C22×C4⋊C4C22×C1111yescharacteristic
253#481—24no—
254C2×#106C22×C1111yescharacteristic, complemented
255C2×#106C22×C1111yescharacteristic, complemented
256C2×C4⋊C8C22×C1112yescomplemented
257C2×#102—24no—
258C2×#102C22×C1112yes—
259C2×#102C22×C1112yes—
260C2×#102C22×C1112yes—
261C2×#102C22×C1112yes—
262C2×#102C22×C1111yescharacteristic, complemented
263C2×#102C22×C1111yescharacteristic, complemented
264C2×#102C22×C1112yescomplemented
265C2×C22⋊C8C22×C1111yescharacteristic
266#392—22no—
267#390C22×C1112yes—
268#389C22×C1112yescomplemented
269#387—22no—
270#380—21no—
271#380C22×C1111yescharacteristic
272C4×C4⋊C4C22×C1112yescomplemented
273C4×C22⋊C4—21no—
274C4×C22⋊C4C22×C1111yescharacteristic
275#340C22×C1112yescomplemented
276#336C22×C1112yescomplemented
277C22×C11—22no—
278C22×C11—24no—
279C22×C11—22no—
280C22×C11—24no—
281C22×C11—44no—
282C22×C11—44no—
283C22×C11—44no—
284C22×C11—816no—
285C22×C11—82no—
286C22×C11—82no—
287C22×C11—82no—
288C22×C11—82no—
289C22×C11—81no—
290C22×C11—81no—
291C22×C11—82no—
292C22×C11—81no—
293C22×C11—82no—
294C22×C11#46014yes—
295C22×C11C2×#12111yescharacteristic
296C22×C11#54612yes—
297C22×C11C22×SD1611yescharacteristic
298C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
299C22×C11#57612yes—
300C4×C11—22no—
301C4×C11—24no—
302C4×C11—42no—
303C4×C11—42no—
304C4×C11—42no—
305C4×C11—81no—
306C4×C11—82no—
307C4×C11#52511yescharacteristic
308C4×C11#53511yescharacteristic
309C4×C11#55112yes—
310C25—21no—
311C22×D4—24no—
312C22×D4—21no—
313C22×D4—22no—
314C22×D4—21no—
315C22×D4—22no—
316C22×D4—22no—
317C22×D4—22no—
318C22×D4—42no—
319C22×D4C23×C1111yescharacteristic
320C22×D4C23×C1112yes—
321C23×C4—21no—
322C23×C4C23×C1111yescharacteristic
323C22×C8—22no—
324C22×C8—42no—
325C22×C8C23×C1112yes—
326C22×C8C23×C1111yescharacteristic
327C22×C8C23×C1111yescharacteristic
328#127—24no—
329#127—42no—
330#121—22no—
331#121—22no—
332#120—44no—
333#120—44no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4D4×C1114yescomplemented
338C2×C4⋊C4C23×C1111yescharacteristic
339C2×C4⋊C4C23×C1112yes—
340C2×C4⋊C4C23×C1111yescharacteristic
341C2×C4⋊C4C23×C1111yescharacteristic
342C2×C22⋊C4—21no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4D4×C1111yescharacteristic
347C2×C22⋊C4D4×C1111yescharacteristic
348C2×C42—22no—
349C2×C42C23×C1112yes—
350#106—22no—
351#106—22no—
352C4⋊C8—42no—
353#102—24no—
354#102—24no—
355#102—24no—
356#102—22no—
357#102—22no—
358#102—42no—
359#102—42no—
360C22⋊C8—22no—
361#95—22no—
362#95—22no—
363#95—21no—
364#95D4×C1112yes—
365C2×C11—24no—
366C2×C11—84no—
367C2×C11—161no—
368C2×C11#241111yescharacteristic
369C2×C11C2×#46011yescharacteristic
370C2×C11#304111yescharacteristic
371C2×C11#329512yes—
372C2×C11#331812yes—
373C24—22no—
374C24—21no—
375C24—44no—
376C24—42no—
377C24—42no—
378C24—42no—
379C24—82no—
380C24C2×D4×C1111yescharacteristic
381C2×D4—28no—
382C2×D4—22no—
383C2×D4—21no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—21no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—48no—
392C2×D4—44no—
393C2×D4—44no—
394C2×D4—44no—
395C2×D4—44no—
396C2×D4—44no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—42no—
400C2×D4—42no—
401C2×D4—44no—
402C2×D4—82no—
403C2×D4—82no—
404C2×D4C11×#4114yes—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—24no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—82no—
413C22×C4C2×D4×C1112yes—
414C22×C4C2×D4×C1111yescharacteristic
415C22×C4C2×D4×C1112yes—
416C22×C4C2×D4×C1112yes—
417C22×C4C11×#4112yes—
418C22×C4C24×C1111yescharacteristic
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—22no—
424C2×C8—22no—
425C2×C8—22no—
426C2×C8—44no—
427C4⋊C4—24no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—22no—
432C4⋊C4—21no—
433C4⋊C4—22no—
434C4⋊C4—82no—
435C4⋊C4C2×D4×C1112yes—
436C4⋊C4C2×D4×C1112yes—
437C22⋊C4—22no—
438C22⋊C4—44no—
439C22⋊C4—42no—
440C22⋊C4—42no—
441C22⋊C4—44no—
442C22⋊C4C11×SD1614yes—
443C42—22no—
444C42—22no—
445C42—82no—
446C11#2447811yescharacteristic, direct product factor, Sylow
447C23—22no—
448C23—22no—
449C23—24no—
450C23—48no—
451C23—42no—
452C23—42no—
453C23—42no—
454C23—42no—
455C23—42no—
456C23—42no—
457C23—41no—
458C23—42no—
459C23—41no—
460C23—41no—
461C23—42no—
462C23—88no—
463C23—88no—
464C23—84no—
465C23—84no—
466C23C11×#12112yes—
467C23C2×C11×SD1612yes—
468C23C11×AGL(1,ℤ/8)12yes—
469C23C22×D4×C1111yescharacteristic
470D4—24no—
471D4—24no—
472D4—48no—
473D4—41no—
474D4—42no—
475D4—41no—
476D4—42no—
477D4—42no—
478D4—88no—
479D4—88no—
480D4—84no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—84no—
501C2×C4C11×#12112yes—
502C2×C4C2×C11×SD1614yes—
503C2×C4C22×D4×C1111yescharacteristic
504C2×C4C2×C11×#4112yes—
505C2×C4C2×C11×#4111yescharacteristic
506C2×C4C11×H(5,𝔽2)12yes—
507C8—41no—
508C8—42no—
509C8—41no—
510C22—22no—
511C22—24no—
512C22—22no—
513C22—24no—
514C22—44no—
515C22—44no—
516C22—44no—
517C22—816no—
518C22—82no—
519C22—82no—
520C22—82no—
521C22—82no—
522C22—81no—
523C22—81no—
524C22—82no—
525C22—81no—
526C22—82no—
527C22C11×#46014yes—
528C22C2×C11×#12111yescharacteristic
529C22C11×#54612yes—
530C22C22×C11×SD1611yescharacteristic
531C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
532C22C11×#57612yes—
533C4—22no—
534C4—24no—
535C4—42no—
536C4—42no—
537C4—42no—
538C4—81no—
539C4—82no—
540C4C11×#52511yescharacteristic
541C4C11×#53511yescharacteristic
542C4C11×#55112yes—
543C2—24no—
544C2—84no—
545C2—161no—
546C2C11×#241111yescharacteristic
547C2C2×C11×#46011yescharacteristic
548C2C11×#304111yescharacteristic
549C2C11×#329512yes—
550C2C11×#331812yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2433C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#481C2semidirect
2. C22×C11×#102C2semidirect
4. C11×#2345C2semidirect
5. C11×#2065C2semidirect
6. C11×#2041C2semidirect
7. C11×#1982C2semidirect
8. C11×#1926C2semidirect
9. C11×#1893C2semidirect
10. C11×#1850C2semidirect
11. C11×#1786C2semidirect
20. C2×C11×#106C22semidirect
21. C2×C11×#106C22semidirect
22. C2×C11×C4⋊C8C22semidirect
28. C2×C11×#102C22semidirect
29. C2×C11×#102C22semidirect
30. C2×C11×#102C22semidirect
34. C11×#389C22semidirect
38. C4×C11×C4⋊C4C22semidirect
41. C11×#340C22semidirect
42. C11×#336C22semidirect
70. C2×C11×C4⋊C4D4semidirect
98. #24478C11direct (N × H)
172. C2×#481C2×C11semidirect
173. C22×#102C2×C11semidirect
175. #2345C2×C11semidirect
176. #2065C2×C11semidirect
177. #2041C2×C11semidirect
178. #1982C2×C11semidirect
179. #1926C2×C11semidirect
180. #1893C2×C11semidirect
181. #1850C2×C11semidirect
182. #1786C2×C11semidirect
254. C2×#106C22×C11semidirect
255. C2×#106C22×C11semidirect
256. C2×C4⋊C8C22×C11semidirect
262. C2×#102C22×C11semidirect
263. C2×#102C22×C11semidirect
264. C2×#102C22×C11semidirect
268. #389C22×C11semidirect
272. C4×C4⋊C4C22×C11semidirect
275. #340C22×C11semidirect
276. #336C22×C11semidirect
337. C2×C4⋊C4D4×C11semidirect
446. C11#24478direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4812
C22×C11×#1022
C11×#24332
C11×#23452
C11×#20652
C11×#20412
C11×#19822
C11×#19262
C11×#18932
C11×#18502
C11×#17862
#2447811