Finite Group Databasebeta

← C11×#24495 #14601688

Subgroups — C11×#24495 #14601688

Order 2816.

1068 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#485C211yesmaximal, characteristic, complemented
2C2×C11×#418C211yesmaximal, characteristic
3C11×#2435C211yesmaximal, characteristic
4C11×#2346C211yesmaximal, characteristic, complemented
5C11×#2067C212yesmaximal, complemented
6C11×#2042C212yesmaximal, complemented
7C11×#1983C212yesmaximal, complemented
8C11×#1926C212yesmaximal, complemented
9C11×#1894C211yesmaximal, characteristic, complemented
10C11×#1851C211yesmaximal, characteristic, complemented
11C11×#1786C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C2×C11×#124C2212yes—
15C2×C11×C22⋊Q8C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C11×#485—24no—
18C2×C11×#107C2211yescharacteristic, complemented
19C2×C11×#106C2211yescharacteristic, complemented
20C2×C11×C4⋊C8C2212yescomplemented
21C11×#418—24no—
22C2×C11×#103C2211yescharacteristic, complemented
23C2×C11×#103C2211yescharacteristic, complemented
24C2×C11×#103C2212yescomplemented
25C2×C11×#102C2212yes—
26C2×C11×#102C2212yes—
27C2×C11×#102C2212yes—
28C2×C11×#102C2212yes—
29C2×C11×C22⋊C8C2211yescharacteristic
30C11×#394—21no—
31C11×#394—21no—
32C11×#390C2212yes—
33C11×#389C2212yescomplemented
34C11×#388—22no—
35C11×#382—21no—
36C11×#380C2211yescharacteristic
37C11×#379—22no—
38C4×C11×C4⋊C4C2212yescomplemented
39C4×C11×C22⋊C4C2211yescharacteristic
40C11×#376—21no—
41C11×#340C2212yescomplemented
42C11×#336C2212yescomplemented
43C25×C11—21no—
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11—24no—
46C22×D4×C11—22no—
47C22×D4×C11—21no—
48C22×D4×C11—22no—
49C22×D4×C11—42no—
50C22×D4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C2×C11×M16—22no—
53C2×C11×M16—42no—
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2312yes—
56C22×C8×C11C2311yescharacteristic
57C11×#124—24no—
58C11×#124—42no—
59C11×C22⋊Q8—22no—
60C11×C22⋊Q8—22no—
61C11×#117—22no—
62C11×#117D414yes—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4D412yes—
77C2×C42×C11—21no—
78C2×C42×C11—22no—
79C2×C42×C11C2312yes—
80C11×#107—22no—
81C11×#106—22no—
82C11×C4⋊C8—42no—
83C11×#103—22no—
84C11×#103—22no—
85C11×#103—42no—
86C11×#102—24no—
87C11×#102—24no—
88C11×#102—24no—
89C11×#102—42no—
90C11×C22⋊C8—22no—
91C11×#95—21no—
92C11×#95—22no—
93C11×#95—22no—
94C11×#95D411yescharacteristic
95C11×#95D411yescharacteristic
96#24495C1111yesmaximal, characteristic, direct product factor, Sylow
97C24×C11—22no—
98C24×C11—44no—
99C24×C11—44no—
100C24×C11—42no—
101C24×C11—81no—
102C24×C11—81no—
103C24×C11C2×D411yescharacteristic
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×D4×C11—28no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—48no—
115C2×D4×C11—44no—
116C2×D4×C11—44no—
117C2×D4×C11—42no—
118C2×D4×C11#4114yes—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D412yes—
130C22×C4×C11#4112yes—
131C22×C4×C11C2411yescharacteristic
132C11×M16—44no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—42no—
147C11×C4⋊C4—82no—
148C11×C4⋊C4C2×D412yes—
149C11×C4⋊C4C2×D412yes—
150C11×C22⋊C4—24no—
151C11×C22⋊C4—42no—
152C11×C22⋊C4—44no—
153C11×C22⋊C4—44no—
154C11×C22⋊C4—42no—
155C11×C22⋊C4—82no—
156C11×C22⋊C4—82no—
157C11×C22⋊C4—81no—
158C42×C11—24no—
159C42×C11—22no—
160C42×C11—22no—
161C42×C11—44no—
162C2×#485C2×C1111yescharacteristic, complemented
163C2×#418C2×C1111yescharacteristic
164#2435C2×C1111yescharacteristic
165#2346C2×C1111yescharacteristic, complemented
166#2067C2×C1112yescomplemented
167#2042C2×C1112yescomplemented
168#1983C2×C1112yescomplemented
169#1926C2×C1112yescomplemented
170#1894C2×C1111yescharacteristic, complemented
171#1851C2×C1111yescharacteristic, complemented
172#1786C2×C1111yescharacteristic
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—21no—
176C23×C11—21no—
177C23×C11—24no—
178C23×C11—48no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11—84no—
186C23×C11—84no—
187C23×C11—88no—
188C23×C11—88no—
189C23×C11#12112yes—
190C23×C11C22×D411yescharacteristic
191Q8×C11—41no—
192Q8×C11—41no—
193Q8×C11—42no—
194D4×C11—24no—
195D4×C11—24no—
196D4×C11—48no—
197D4×C11—42no—
198D4×C11—42no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—24no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—42no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—41no—
220C2×C4×C11—42no—
221C2×C4×C11—41no—
222C2×C4×C11#12112yes—
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C2×#4112yes—
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11H(5,𝔽2)12yes—
227C8×C11—41no—
228C8×C11—41no—
229C8×C11—42no—
230C23×D4C22×C1111yescharacteristic
231C22×M16C22×C1111yescharacteristic
232C2×#124C22×C1112yes—
233C2×C22⋊Q8C22×C1111yescharacteristic
234C2×#117C22×C1111yescharacteristic
235#485—24no—
236C2×#107C22×C1111yescharacteristic, complemented
237C2×#106C22×C1111yescharacteristic, complemented
238C2×C4⋊C8C22×C1112yescomplemented
239#418—24no—
240C2×#103C22×C1111yescharacteristic, complemented
241C2×#103C22×C1111yescharacteristic, complemented
242C2×#103C22×C1112yescomplemented
243C2×#102C22×C1112yes—
244C2×#102C22×C1112yes—
245C2×#102C22×C1112yes—
246C2×#102C22×C1112yes—
247C2×C22⋊C8C22×C1111yescharacteristic
248#394—21no—
249#394—21no—
250#390C22×C1112yes—
251#389C22×C1112yescomplemented
252#388—22no—
253#382—21no—
254#380C22×C1111yescharacteristic
255#379—22no—
256C4×C4⋊C4C22×C1112yescomplemented
257C4×C22⋊C4C22×C1111yescharacteristic
258#376—21no—
259#340C22×C1112yescomplemented
260#336C22×C1112yescomplemented
261C22×C11—22no—
262C22×C11—22no—
263C22×C11—22no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11—44no—
267C22×C11—44no—
268C22×C11—44no—
269C22×C11—816no—
270C22×C11—82no—
271C22×C11—82no—
272C22×C11—82no—
273C22×C11—82no—
274C22×C11C2×#12111yescharacteristic
275C22×C11#54612yes—
276C22×C11#57512yes—
277C22×C11#57611yescharacteristic
278C22×C11#57711yescharacteristic
279C4×C11—22no—
280C4×C11—42no—
281C4×C11—42no—
282C4×C11—42no—
283C4×C11—42no—
284C4×C11—81no—
285C4×C11—81no—
286C4×C11—82no—
287C4×C11#52511yescharacteristic
288C4×C11#53511yescharacteristic
289C4×C11#55112yes—
290C25—21no—
291C22×Q8C23×C1111yescharacteristic
292C22×D4—24no—
293C22×D4—22no—
294C22×D4—21no—
295C22×D4—22no—
296C22×D4—42no—
297C22×D4C23×C1112yes—
298C23×C4C23×C1111yescharacteristic
299C2×M16—22no—
300C2×M16—42no—
301C22×C8C23×C1112yes—
302C22×C8C23×C1111yescharacteristic
303C22×C8C23×C1111yescharacteristic
304#124—24no—
305#124—42no—
306C22⋊Q8—22no—
307C22⋊Q8—22no—
308#117—22no—
309#117D4×C1114yes—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4C23×C1111yescharacteristic
313C2×C4⋊C4C23×C1112yes—
314C2×C4⋊C4C23×C1111yescharacteristic
315C2×C4⋊C4C23×C1111yescharacteristic
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4D4×C1112yes—
324C2×C42—21no—
325C2×C42—22no—
326C2×C42C23×C1112yes—
327#107—22no—
328#106—22no—
329C4⋊C8—42no—
330#103—22no—
331#103—22no—
332#103—42no—
333#102—24no—
334#102—24no—
335#102—24no—
336#102—42no—
337C22⋊C8—22no—
338#95—21no—
339#95—22no—
340#95—22no—
341#95D4×C1111yescharacteristic
342#95D4×C1111yescharacteristic
343C2×C11—42no—
344C2×C11—84no—
345C2×C11#241111yescharacteristic
346C2×C11#304011yescharacteristic
347C2×C11#304511yescharacteristic
348C2×C11#331912yes—
349C2×C11#332312yes—
350C24—22no—
351C24—44no—
352C24—44no—
353C24—42no—
354C24—81no—
355C24—81no—
356C24C2×D4×C1111yescharacteristic
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—22no—
360C2×Q8—22no—
361C2×D4—28no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—48no—
368C2×D4—44no—
369C2×D4—44no—
370C2×D4—42no—
371C2×D4C11×#4114yes—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4C2×D4×C1112yes—
380C22×C4C2×D4×C1112yes—
381C22×C4C2×D4×C1111yescharacteristic
382C22×C4C2×D4×C1112yes—
383C22×C4C11×#4112yes—
384C22×C4C24×C1111yescharacteristic
385M16—44no—
386C2×C8—21no—
387C2×C8—21no—
388C2×C8—22no—
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—22no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—22no—
397C4⋊C4—21no—
398C4⋊C4—22no—
399C4⋊C4—42no—
400C4⋊C4—82no—
401C4⋊C4C2×D4×C1112yes—
402C4⋊C4C2×D4×C1112yes—
403C22⋊C4—24no—
404C22⋊C4—42no—
405C22⋊C4—44no—
406C22⋊C4—44no—
407C22⋊C4—42no—
408C22⋊C4—82no—
409C22⋊C4—82no—
410C22⋊C4—81no—
411C42—24no—
412C42—22no—
413C42—22no—
414C42—44no—
415C11#2449511yescharacteristic, direct product factor, Sylow
416C23—22no—
417C23—22no—
418C23—21no—
419C23—21no—
420C23—24no—
421C23—48no—
422C23—42no—
423C23—42no—
424C23—42no—
425C23—42no—
426C23—42no—
427C23—42no—
428C23—84no—
429C23—84no—
430C23—88no—
431C23—88no—
432C23C11×#12112yes—
433C23C22×D4×C1111yescharacteristic
434Q8—41no—
435Q8—41no—
436Q8—42no—
437D4—24no—
438D4—24no—
439D4—48no—
440D4—42no—
441D4—42no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—24no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—41no—
463C2×C4—42no—
464C2×C4—41no—
465C2×C4C11×#12112yes—
466C2×C4C22×D4×C1111yescharacteristic
467C2×C4C2×C11×#4112yes—
468C2×C4C2×C11×#4111yescharacteristic
469C2×C4C11×H(5,𝔽2)12yes—
470C8—41no—
471C8—42no—
472C8—41no—
473C22—22no—
474C22—22no—
475C22—22no—
476C22—42no—
477C22—42no—
478C22—44no—
479C22—44no—
480C22—44no—
481C22—816no—
482C22—82no—
483C22—82no—
484C22—82no—
485C22—82no—
486C22C2×C11×#12111yescharacteristic
487C22C11×#54612yes—
488C22C11×#57512yes—
489C22C11×#57611yescharacteristic
490C22C11×#57711yescharacteristic
491C4—22no—
492C4—42no—
493C4—42no—
494C4—42no—
495C4—42no—
496C4—81no—
497C4—81no—
498C4—82no—
499C4C11×#52511yescharacteristic
500C4C11×#53511yescharacteristic
501C4C11×#55112yes—
502C2—42no—
503C2—84no—
504C2C11×#241111yescharacteristic
505C2C11×#304011yescharacteristic
506C2C11×#304511yescharacteristic
507C2C11×#331912yes—
508C2C11×#332312yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC23×D4×C11C22
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×#485C2semidirect
4. C11×#2346C2semidirect
5. C11×#2067C2semidirect
6. C11×#2042C2semidirect
7. C11×#1983C2semidirect
8. C11×#1926C2semidirect
9. C11×#1894C2semidirect
10. C11×#1851C2semidirect
18. C2×C11×#107C22semidirect
19. C2×C11×#106C22semidirect
20. C2×C11×C4⋊C8C22semidirect
22. C2×C11×#103C22semidirect
23. C2×C11×#103C22semidirect
24. C2×C11×#103C22semidirect
33. C11×#389C22semidirect
38. C4×C11×C4⋊C4C22semidirect
41. C11×#340C22semidirect
42. C11×#336C22semidirect
96. #24495C11direct (N × H)
162. C2×#485C2×C11semidirect
165. #2346C2×C11semidirect
166. #2067C2×C11semidirect
167. #2042C2×C11semidirect
168. #1983C2×C11semidirect
169. #1926C2×C11semidirect
170. #1894C2×C11semidirect
171. #1851C2×C11semidirect
236. C2×#107C22×C11semidirect
237. C2×#106C22×C11semidirect
238. C2×C4⋊C8C22×C11semidirect
240. C2×#103C22×C11semidirect
241. C2×#103C22×C11semidirect
242. C2×#103C22×C11semidirect
251. #389C22×C11semidirect
256. C4×C4⋊C4C22×C11semidirect
259. #340C22×C11semidirect
260. #336C22×C11semidirect
415. C11#24495direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4852
C2×C11×#4182
C11×#24352
C11×#23462
C11×#20672
C11×#20422
C11×#19832
C11×#19262
C11×#18942
C11×#18512
C11×#17862
#2449511