Finite Group Databasebeta

← C11×#20959 #14598152

Subgroups — C11×#20959 #14598152

Order 2816.

1974 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#525C211yesmaximal, characteristic
2C11×#3428C211yesmaximal, characteristic, complemented
3C2×C11×#410C211yesmaximal, characteristic, complemented
4C11×#2280C212yesmaximal, complemented
5C11×#1890C214yesmaximal, complemented
6C11×#1889C214yesmaximal, complemented
7C11×#1740C212yesmaximal, complemented
8C22×C11×#41C2211yescharacteristic
9C24×C4×C11C2211yescharacteristic
10C11×#525—24no—
11C11×#525C418yescomplemented
12C2×C11×#123C2212yes—
13C2×C11×C22⋊Q8—21no—
14C2×C11×#121—21no—
15C2×C11×#120C2212yes—
16C11×#520—24no—
17C11×#519—21no—
18C11×#518—21no—
19C11×#518C2214yes—
20C4×C11×#41—24no—
21C2×C4×D4×C11—22no—
22C2×C11×#117—22no—
23C2×C11×#117C2212yes—
24C2×C11×#117C2211yescharacteristic
25C2×C11×#117C2212yes—
26C11×#410—24no—
27C2×C11×#99C2214yes—
28C11×#381C2214yes—
29C11×#380—24no—
30C11×#379C2214yes—
31C4×C11×C22⋊C4—24no—
32C11×#342C2218yes—
33C25×C11C2311yescharacteristic
34C2×C11×#41—22no—
35C2×C11×#41—22no—
36C2×C11×#41—24no—
37C2×C11×#41C2×C414yes—
38C2×C11×#41D414yes—
39C22×Q8×C11D411yescharacteristic
40C22×D4×C11—22no—
41C22×D4×C11D411yescharacteristic
42C22×D4×C11C2312yes—
43C23×C4×C11—22no—
44C23×C4×C11—21no—
45C23×C4×C11—22no—
46C23×C4×C11—21no—
47C23×C4×C11—22no—
48C23×C4×C11—24no—
49C23×C4×C11C2×C414yescomplemented
50C23×C4×C11D412yes—
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C11×#123—24no—
54C11×#123C2×C418yescomplemented
55C11×C22⋊Q8—28no—
56C11×#121—28no—
57C11×#120—24no—
58C11×#120C2×C418yescomplemented
59C4×Q8×C11—28no—
60C4×D4×C11—28no—
61C4×D4×C11—216no—
62C4×D4×C11—216no—
63C11×#117—24no—
64C11×#117—24no—
65C11×#117—22no—
66C11×#117—24no—
67C11×#117—22no—
68C11×#117—22no—
69C11×#117—22no—
70C11×#117—22no—
71C11×#117—24no—
72C11×#117—24no—
73C11×#117C2×C414yescomplemented
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4D414yescomplemented
79C2×C11×C22⋊C4—24no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—28no—
83C2×C11×C22⋊C4C2314yes—
84C2×C11×C22⋊C4C2314yes—
85C2×C11×C22⋊C4C2312yes—
86C2×C42×C11—24no—
87C2×C42×C11—21no—
88C2×C42×C11—22no—
89C2×C42×C11D414yescomplemented
90C11×#99—28no—
91C11×#95—28no—
92#20959C1111yesmaximal, characteristic, direct product factor, Sylow
93C24×C11—22no—
94C24×C11—21no—
95C24×C11—21no—
96C24×C11—22no—
97C24×C11—44no—
98C24×C11C22×C412yes—
99C24×C11C2×D412yes—
100C24×C11C2411yescharacteristic
101C11×#41—28no—
102C11×#41—28no—
103C11×#41—28no—
104C11×#41—28no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11C22⋊C414yescomplemented
108C2×D4×C11—24no—
109C2×D4×C11—24no—
110C2×D4×C11—28no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—48no—
114C2×D4×C11C22⋊C414yescomplemented
115C2×D4×C11C22×C414yes—
116C2×D4×C11C2×D414yes—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—24no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—28no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—28no—
129C22×C4×C11—28no—
130C22×C4×C11—24no—
131C22×C4×C11—42no—
132C22×C4×C11—41no—
133C22×C4×C11—41no—
134C22×C4×C11—44no—
135C22×C4×C11—44no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11C22⋊C418yescomplemented
139C22×C4×C11C22×C412yes—
140C22×C4×C11C22×C412yes—
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D418yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D412yes—
148C22×C4×C11#4114yes—
149C11×C4⋊C4—28no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—28no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—44no—
155C11×C22⋊C4—28no—
156C11×C22⋊C4—28no—
157C11×C22⋊C4—24no—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—28no—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—416no—
164C11×C22⋊C4C22×C414yes—
165C42×C11—28no—
166C42×C11—24no—
167C42×C11—24no—
168C42×C11—24no—
169C42×C11—44no—
170C2×#525C2×C1111yescharacteristic
171#3428C2×C1111yescharacteristic, complemented
172C2×#410C2×C1111yescharacteristic, complemented
173#2280C2×C1112yescomplemented
174#1890C2×C1114yescomplemented
175#1889C2×C1114yescomplemented
176#1740C2×C1112yescomplemented
177C23×C11—28no—
178C23×C11—24no—
179C23×C11—22no—
180C23×C11—24no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—44no—
184C23×C11—42no—
185C23×C11—44no—
186C23×C11—42no—
187C23×C11—44no—
188C23×C11—48no—
189C23×C11—44no—
190C23×C11—41no—
191C23×C11—42no—
192C23×C11—41no—
193C23×C11C2×C22⋊C414yes—
194C23×C11C23×C411yescharacteristic
195C23×C11C22×D411yescharacteristic
196C23×C11C22×D412yes—
197C23×C11C22×D411yescharacteristic
198C23×C11C2×#4112yes—
199Q8×C11—28no—
200D4×C11—28no—
201D4×C11—28no—
202D4×C11—28no—
203D4×C11—416no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—28no—
207C2×C4×C11—28no—
208C2×C4×C11—24no—
209C2×C4×C11—22no—
210C2×C4×C11—24no—
211C2×C4×C11—28no—
212C2×C4×C11—44no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—41no—
216C2×C4×C11—44no—
217C2×C4×C11—44no—
218C2×C4×C11—48no—
219C2×C4×C11—48no—
220C2×C4×C11—48no—
221C2×C4×C11—44no—
222C2×C4×C11—88no—
223C2×C4×C11C2×C22⋊C414yes—
224C2×C4×C11C2×C22⋊C412yes—
225C2×C4×C11C2×C22⋊C412yes—
226C2×C4×C11C4×D414yes—
227C2×C4×C11C4×D414yes—
228C2×C4×C11#12012yes—
229C2×C4×C11#12011yescharacteristic
230C2×C4×C11#12011yescharacteristic
231C2×C4×C11#12114yes—
232C2×C4×C11#12114yes—
233C2×C4×C11#12312yes—
234C2×C4×C11#12312yes—
235C22×#41C22×C1111yescharacteristic
236C24×C4C22×C1111yescharacteristic
237#525—24no—
238#525C4×C1118yescomplemented
239C2×#123C22×C1112yes—
240C2×C22⋊Q8—21no—
241C2×#121—21no—
242C2×#120C22×C1112yes—
243#520—24no—
244#519—21no—
245#518—21no—
246#518C22×C1114yes—
247C4×#41—24no—
248C2×C4×D4—22no—
249C2×#117—22no—
250C2×#117C22×C1112yes—
251C2×#117C22×C1111yescharacteristic
252C2×#117C22×C1112yes—
253#410—24no—
254C2×#99C22×C1114yes—
255#381C22×C1114yes—
256#380—24no—
257#379C22×C1114yes—
258C4×C22⋊C4—24no—
259#342C22×C1118yes—
260C22×C11—24no—
261C22×C11—22no—
262C22×C11—24no—
263C22×C11—28no—
264C22×C11—24no—
265C22×C11—41no—
266C22×C11—41no—
267C22×C11—42no—
268C22×C11—44no—
269C22×C11—42no—
270C22×C11—48no—
271C22×C11—44no—
272C22×C11—44no—
273C22×C11—44no—
274C22×C11—44no—
275C22×C11—42no—
276C22×C11—82no—
277C22×C11C22×C22⋊C411yescharacteristic
278C22×C11C2×C4×D412yes—
279C22×C11C2×#12011yescharacteristic
280C22×C11C2×#12112yes—
281C22×C11C2×#12311yescharacteristic
282C4×C11—24no—
283C4×C11—44no—
284C4×C11—48no—
285C4×C11—42no—
286C4×C11—84no—
287C4×C11#38612yes—
288C4×C11#38612yes—
289C4×C11#38614yes—
290C25C23×C1111yescharacteristic
291C2×#41—22no—
292C2×#41—22no—
293C2×#41—24no—
294C2×#41C2×C4×C1114yes—
295C2×#41D4×C1114yes—
296C22×Q8D4×C1111yescharacteristic
297C22×D4—22no—
298C22×D4D4×C1111yescharacteristic
299C22×D4C23×C1112yes—
300C23×C4—21no—
301C23×C4—21no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—24no—
306C23×C4C2×C4×C1114yescomplemented
307C23×C4D4×C1112yes—
308C23×C4C23×C1111yescharacteristic
309C23×C4C23×C1111yescharacteristic
310#123—24no—
311#123C2×C4×C1118yescomplemented
312C22⋊Q8—28no—
313#121—28no—
314#120—24no—
315#120C2×C4×C1118yescomplemented
316C4×Q8—28no—
317C4×D4—28no—
318C4×D4—216no—
319C4×D4—216no—
320#117—24no—
321#117—24no—
322#117—22no—
323#117—24no—
324#117—22no—
325#117—22no—
326#117—22no—
327#117—22no—
328#117—24no—
329#117—24no—
330#117C2×C4×C1114yescomplemented
331C2×C4⋊C4—24no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4D4×C1114yescomplemented
336C2×C22⋊C4—24no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4C23×C1114yes—
341C2×C22⋊C4C23×C1114yes—
342C2×C22⋊C4C23×C1112yes—
343C2×C42—24no—
344C2×C42—21no—
345C2×C42—22no—
346C2×C42D4×C1114yescomplemented
347#99—28no—
348#95—28no—
349C2×C11—21no—
350C2×C11—22no—
351C2×C11—22no—
352C2×C11—21no—
353C2×C11—44no—
354C2×C11—44no—
355C2×C11C2×#38611yescharacteristic
356C2×C11#302512yes—
357C24—22no—
358C24—21no—
359C24—21no—
360C24—22no—
361C24—44no—
362C24C22×C4×C1112yes—
363C24C2×D4×C1112yes—
364C24C24×C1111yescharacteristic
365#41—28no—
366#41—28no—
367#41—28no—
368#41—28no—
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8C11×C22⋊C414yescomplemented
372C2×D4—24no—
373C2×D4—24no—
374C2×D4—28no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—48no—
378C2×D4C11×C22⋊C414yescomplemented
379C2×D4C22×C4×C1114yes—
380C2×D4C2×D4×C1114yes—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—24no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—28no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—28no—
393C22×C4—28no—
394C22×C4—24no—
395C22×C4—42no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—44no—
399C22×C4—44no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4C11×C22⋊C418yescomplemented
403C22×C4C22×C4×C1112yes—
404C22×C4C22×C4×C1112yes—
405C22×C4C2×D4×C1112yes—
406C22×C4C2×D4×C1118yes—
407C22×C4C2×D4×C1111yescharacteristic
408C22×C4C2×D4×C1111yescharacteristic
409C22×C4C2×D4×C1112yes—
410C22×C4C2×D4×C1112yes—
411C22×C4C2×D4×C1112yes—
412C22×C4C11×#4114yes—
413C4⋊C4—28no—
414C4⋊C4—24no—
415C4⋊C4—28no—
416C4⋊C4—24no—
417C4⋊C4—24no—
418C4⋊C4—44no—
419C22⋊C4—28no—
420C22⋊C4—28no—
421C22⋊C4—24no—
422C22⋊C4—24no—
423C22⋊C4—22no—
424C22⋊C4—28no—
425C22⋊C4—24no—
426C22⋊C4—24no—
427C22⋊C4—416no—
428C22⋊C4C22×C4×C1114yes—
429C42—28no—
430C42—24no—
431C42—24no—
432C42—24no—
433C42—44no—
434C11#2095911yescharacteristic, direct product factor, Sylow
435C23—28no—
436C23—24no—
437C23—22no—
438C23—24no—
439C23—22no—
440C23—22no—
441C23—44no—
442C23—42no—
443C23—44no—
444C23—42no—
445C23—44no—
446C23—48no—
447C23—44no—
448C23—41no—
449C23—42no—
450C23—41no—
451C23C2×C11×C22⋊C414yes—
452C23C23×C4×C1111yescharacteristic
453C23C22×D4×C1111yescharacteristic
454C23C22×D4×C1112yes—
455C23C22×D4×C1111yescharacteristic
456C23C2×C11×#4112yes—
457Q8—28no—
458D4—28no—
459D4—28no—
460D4—28no—
461D4—416no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—28no—
465C2×C4—28no—
466C2×C4—24no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—28no—
470C2×C4—44no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—41no—
474C2×C4—44no—
475C2×C4—44no—
476C2×C4—48no—
477C2×C4—48no—
478C2×C4—48no—
479C2×C4—44no—
480C2×C4—88no—
481C2×C4C2×C11×C22⋊C414yes—
482C2×C4C2×C11×C22⋊C412yes—
483C2×C4C2×C11×C22⋊C412yes—
484C2×C4C4×D4×C1114yes—
485C2×C4C4×D4×C1114yes—
486C2×C4C11×#12012yes—
487C2×C4C11×#12011yescharacteristic
488C2×C4C11×#12011yescharacteristic
489C2×C4C11×#12114yes—
490C2×C4C11×#12114yes—
491C2×C4C11×#12312yes—
492C2×C4C11×#12312yes—
493C22—24no—
494C22—22no—
495C22—24no—
496C22—28no—
497C22—24no—
498C22—41no—
499C22—41no—
500C22—42no—
501C22—44no—
502C22—42no—
503C22—48no—
504C22—44no—
505C22—44no—
506C22—44no—
507C22—44no—
508C22—42no—
509C22—82no—
510C22C22×C11×C22⋊C411yescharacteristic
511C22C2×C4×D4×C1112yes—
512C22C2×C11×#12011yescharacteristic
513C22C2×C11×#12112yes—
514C22C2×C11×#12311yescharacteristic
515C4—24no—
516C4—44no—
517C4—48no—
518C4—42no—
519C4—84no—
520C4C11×#38612yes—
521C4C11×#38612yes—
522C4C11×#38614yes—
523C2—21no—
524C2—22no—
525C2—22no—
526C2—21no—
527C2—44no—
528C2—44no—
529C2C2×C11×#38611yescharacteristic
530C2C11×#302512yes—
subgroupG/H
centerC2×C4×C11#120
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
socleC22×C11C2×#120
prime radicalC2×C11×#525C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3428C2semidirect
3. C2×C11×#410C2semidirect
4. C11×#2280C2semidirect
5. C11×#1890C2semidirect
6. C11×#1889C2semidirect
7. C11×#1740C2semidirect
11. C11×#525C4semidirect
49. C23×C4×C11C2×C4semidirect
54. C11×#123C2×C4semidirect
58. C11×#120C2×C4semidirect
73. C11×#117C2×C4semidirect
78. C2×C11×C4⋊C4D4semidirect
89. C2×C42×C11D4semidirect
92. #20959C11direct (N × H)
107. C2×Q8×C11C22⋊C4semidirect
114. C2×D4×C11C22⋊C4semidirect
138. C22×C4×C11C22⋊C4semidirect
171. #3428C2×C11semidirect
172. C2×#410C2×C11semidirect
173. #2280C2×C11semidirect
174. #1890C2×C11semidirect
175. #1889C2×C11semidirect
176. #1740C2×C11semidirect
238. #525C4×C11semidirect
306. C23×C4C2×C4×C11semidirect
311. #123C2×C4×C11semidirect
315. #120C2×C4×C11semidirect
330. #117C2×C4×C11semidirect
335. C2×C4⋊C4D4×C11semidirect
346. C2×C42D4×C11semidirect
371. C2×Q8C11×C22⋊C4semidirect
378. C2×D4C11×C22⋊C4semidirect
402. C22×C4C11×C22⋊C4semidirect
434. C11#20959direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5252
C11×#34282
C2×C11×#4102
C11×#22802
C11×#18902
C11×#18892
C11×#17402
#2095911