Finite Group Databasebeta

← C11×#22489 #14599682

Subgroups — C11×#22489 #14599682

Order 2816.

1206 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#555C211yesmaximal, characteristic
2C2×C8×D4×C11C211yesmaximal, characteristic, complemented
3C11×#2354C211yesmaximal, characteristic, complemented
4C11×#1990C211yesmaximal, characteristic, complemented
5C11×#1987C211yesmaximal, characteristic, complemented
6C11×#1893C212yesmaximal, complemented
7C11×#1875C212yesmaximal, complemented
8C11×#1825C212yesmaximal, complemented
9C11×#1802C211yesmaximal, characteristic, complemented
10C4×C11×#102C211yesmaximal, characteristic, complemented
11C11×#1735C212yesmaximal, complemented
12C23×C8×C11C2212yes—
13C11×#555—24no—
14C11×#555C418yescomplemented
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#124—22no—
17C2×C11×#121—21no—
18C2×C11×#121C2212yes—
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C11×#117—21no—
22C2×C11×#117C2212yes—
23C2×C11×#117C2212yes—
24C8×D4×C11—24no—
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2212yes—
29C2×C11×C22⋊C8C2212yes—
30C2×C4×C8×C11C2211yescharacteristic
31C11×#390—21no—
32C11×#388—22no—
33C11×#384C2211yescharacteristic
34C11×#380C2212yes—
35C4×C11×C4⋊C4—21no—
36C4×C11×C4⋊C4C2211yescharacteristic
37C11×#340C2212yes—
38C11×#340C2212yes—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2211yescharacteristic
42C11×#340C2212yes—
43C11×#340C2211yescharacteristic
44C22×Q8×C11—21no—
45C22×D4×C11—22no—
46C22×D4×C11D411yescharacteristic
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11—21no—
49C23×C4×C11C2312yes—
50C22×C8×C11—24no—
51C22×C8×C11—24no—
52C22×C8×C11—42no—
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2312yes—
55C22×C8×C11C2311yescharacteristic
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8C2×C414yes—
58C11×#124—216no—
59C11×#121—28no—
60C11×#121—24no—
61C11×#121C2×C418yes—
62C4×D4×C11—22no—
63C4×D4×C11C2×C414yes—
64C4×D4×C11C2×C414yes—
65C4×D4×C11D414yes—
66C11×#117—24no—
67C11×#117—28no—
68C11×#117—24no—
69C11×#117—42no—
70C11×#117C2×C418yes—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4D412yes—
86C2×C42×C11—22no—
87C2×C42×C11—22no—
88C2×C42×C11—21no—
89C2×C42×C11C2311yescharacteristic
90C11×C4⋊C8—22no—
91C11×#102—22no—
92C11×#102—22no—
93C11×#102—42no—
94C11×C22⋊C8—24no—
95C4×C8×C11—22no—
96C11×#95—22no—
97C11×#95—21no—
98#22489C1111yesmaximal, characteristic, direct product factor, Sylow
99C24×C11—21no—
100C24×C11C2×D412yes—
101C2×Q8×C11—24no—
102C2×Q8×C11—81no—
103C2×Q8×C11—81no—
104C2×D4×C11—28no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—21no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—82no—
113C2×D4×C11—82no—
114C2×D4×C11C22⋊C414yes—
115C2×D4×C11C22×C412yes—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—24no—
124C22×C4×C11—21no—
125C22×C4×C11—22no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11C22×C414yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D414yes—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11—22no—
137C2×C8×C11—21no—
138C2×C8×C11—22no—
139C2×C8×C11—21no—
140C2×C8×C11—22no—
141C2×C8×C11—21no—
142C2×C8×C11—48no—
143C2×C8×C11#4112yes—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—42no—
153C11×C4⋊C4—81no—
154C11×C4⋊C4C22⋊C414yes—
155C11×C4⋊C4C22×C412yes—
156C11×C4⋊C4C22×C414yes—
157C11×C4⋊C4#4112yes—
158C11×C22⋊C4—28no—
159C11×C22⋊C4—28no—
160C11×C22⋊C4—24no—
161C11×C22⋊C4—44no—
162C11×C22⋊C4—82no—
163C11×C22⋊C4C22⋊C418yes—
164C42×C11—28no—
165C42×C11—44no—
166C42×C11—42no—
167C42×C11C22×C412yes—
168C42×C11C2×D412yes—
169C2×#555C2×C1111yescharacteristic
170C2×C8×D4C2×C1111yescharacteristic, complemented
171#2354C2×C1111yescharacteristic, complemented
172#1990C2×C1111yescharacteristic, complemented
173#1987C2×C1111yescharacteristic, complemented
174#1893C2×C1112yescomplemented
175#1875C2×C1112yescomplemented
176#1825C2×C1112yescomplemented
177#1802C2×C1111yescharacteristic, complemented
178C4×#102C2×C1111yescharacteristic, complemented
179#1735C2×C1112yescomplemented
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—41no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11C2×C22⋊C414yes—
194C23×C11C22×D411yescharacteristic
195Q8×C11—84no—
196D4×C11—22no—
197D4×C11—22no—
198D4×C11—28no—
199D4×C11—41no—
200D4×C11—41no—
201D4×C11—88no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—22no—
211C2×C4×C11—24no—
212C2×C4×C11—22no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—42no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—48no—
220C2×C4×C11—42no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—42no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11C2×C22⋊C414yes—
227C2×C4×C11C2×C22⋊C412yes—
228C2×C4×C11C2×C22⋊C412yes—
229C2×C4×C11#13512yes—
230C2×C4×C11#13512yes—
231C2×C4×C11C23×C411yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C11H(5,𝔽2)11yescharacteristic
236C2×C4×C112−1+411yescharacteristic
237C8×C11—22no—
238C8×C11—42no—
239C8×C11—41no—
240C23×C8C22×C1112yes—
241#555—24no—
242#555C4×C1118yescomplemented
243C2×C4⋊Q8C22×C1111yescharacteristic
244C2×#124—22no—
245C2×#121—21no—
246C2×#121C22×C1112yes—
247C2×C4×D4C22×C1111yescharacteristic
248C2×C4×D4C22×C1111yescharacteristic
249C2×#117—21no—
250C2×#117C22×C1112yes—
251C2×#117C22×C1112yes—
252C8×D4—24no—
253C2×C4⋊C8C22×C1111yescharacteristic
254C2×#102C22×C1111yescharacteristic
255C2×#102C22×C1111yescharacteristic
256C2×#102C22×C1112yes—
257C2×C22⋊C8C22×C1112yes—
258C2×C4×C8C22×C1111yescharacteristic
259#390—21no—
260#388—22no—
261#384C22×C1111yescharacteristic
262#380C22×C1112yes—
263C4×C4⋊C4—21no—
264C4×C4⋊C4C22×C1111yescharacteristic
265#340C22×C1112yes—
266#340C22×C1111yescharacteristic
267#340C22×C1112yes—
268#340C22×C1112yes—
269#340C22×C1112yes—
270#340C22×C1112yes—
271#340C22×C1111yescharacteristic
272C22×C11—24no—
273C22×C11—24no—
274C22×C11—24no—
275C22×C11—42no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11—42no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—81no—
283C22×C11—81no—
284C22×C11—81no—
285C22×C11—81no—
286C22×C11C22×C22⋊C411yescharacteristic
287C22×C11#54611yescharacteristic
288C22×C11#54711yescharacteristic
289C22×C11C2×#13511yescharacteristic
290C22×C11C2×#13511yescharacteristic
291C22×C11#57611yescharacteristic
292C22×C11#57711yescharacteristic
293C4×C11—24no—
294C4×C11—22no—
295C4×C11—42no—
296C4×C11—44no—
297C4×C11—42no—
298C4×C11—81no—
299C4×C11—82no—
300C4×C11#41614yes—
301C4×C11C4×#4111yescharacteristic
302C4×C11#52011yescharacteristic
303C4×C11#54611yescharacteristic
304C4×C11#54711yescharacteristic
305C22×Q8—21no—
306C22×D4—22no—
307C22×D4D4×C1111yescharacteristic
308C22×D4C23×C1111yescharacteristic
309C23×C4—21no—
310C23×C4C23×C1112yes—
311C22×C8—24no—
312C22×C8—24no—
313C22×C8—42no—
314C22×C8C23×C1112yes—
315C22×C8C23×C1111yescharacteristic
316C22×C8C23×C1111yescharacteristic
317C4⋊Q8—22no—
318C4⋊Q8C2×C4×C1114yes—
319#124—216no—
320#121—28no—
321#121—24no—
322#121C2×C4×C1118yes—
323C4×D4—22no—
324C4×D4C2×C4×C1114yes—
325C4×D4C2×C4×C1114yes—
326C4×D4D4×C1114yes—
327#117—24no—
328#117—28no—
329#117—24no—
330#117—42no—
331#117C2×C4×C1118yes—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4D4×C1111yescharacteristic
336C2×C4⋊C4C23×C1112yes—
337C2×C4⋊C4C23×C1111yescharacteristic
338C2×C4⋊C4C23×C1111yescharacteristic
339C2×C4⋊C4C23×C1112yes—
340C2×C4⋊C4C23×C1111yescharacteristic
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4D4×C1112yes—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—21no—
350C2×C42C23×C1111yescharacteristic
351C4⋊C8—22no—
352#102—22no—
353#102—22no—
354#102—42no—
355C22⋊C8—24no—
356C4×C8—22no—
357#95—22no—
358#95—21no—
359C2×C11—44no—
360C2×C11—82no—
361C2×C11#233911yescharacteristic
362C2×C11C2×#41611yescharacteristic
363C2×C11#289711yescharacteristic
364C2×C11#330311yescharacteristic
365C2×C11#330511yescharacteristic
366C2×C11#334011yescharacteristic
367C2×C11#334111yescharacteristic
368C24—21no—
369C24C2×D4×C1112yes—
370C2×Q8—24no—
371C2×Q8—81no—
372C2×Q8—81no—
373C2×D4—28no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4—21no—
380C2×D4—21no—
381C2×D4—82no—
382C2×D4—82no—
383C2×D4C11×C22⋊C414yes—
384C2×D4C22×C4×C1112yes—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—24no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—42no—
396C22×C4—42no—
397C22×C4C22×C4×C1114yes—
398C22×C4C2×D4×C1112yes—
399C22×C4C2×D4×C1111yescharacteristic
400C22×C4C2×D4×C1114yes—
401C22×C4C2×D4×C1111yescharacteristic
402C22×C4C24×C1111yescharacteristic
403C2×C8—21no—
404C2×C8—21no—
405C2×C8—21no—
406C2×C8—22no—
407C2×C8—21no—
408C2×C8—22no—
409C2×C8—22no—
410C2×C8—21no—
411C2×C8—48no—
412C2×C8C11×#4112yes—
413C4⋊C4—24no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—21no—
421C4⋊C4—42no—
422C4⋊C4—81no—
423C4⋊C4C11×C22⋊C414yes—
424C4⋊C4C22×C4×C1112yes—
425C4⋊C4C22×C4×C1114yes—
426C4⋊C4C11×#4112yes—
427C22⋊C4—28no—
428C22⋊C4—28no—
429C22⋊C4—24no—
430C22⋊C4—44no—
431C22⋊C4—82no—
432C22⋊C4C11×C22⋊C418yes—
433C42—28no—
434C42—44no—
435C42—42no—
436C42C22×C4×C1112yes—
437C42C2×D4×C1112yes—
438C11#2248911yescharacteristic, direct product factor, Sylow
439C23—22no—
440C23—22no—
441C23—22no—
442C23—22no—
443C23—22no—
444C23—22no—
445C23—22no—
446C23—41no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23—41no—
452C23C2×C11×C22⋊C414yes—
453C23C22×D4×C1111yescharacteristic
454Q8—84no—
455D4—22no—
456D4—22no—
457D4—28no—
458D4—41no—
459D4—41no—
460D4—88no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—22no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—48no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4C2×C11×C22⋊C414yes—
486C2×C4C2×C11×C22⋊C412yes—
487C2×C4C2×C11×C22⋊C412yes—
488C2×C4C11×#13512yes—
489C2×C4C11×#13512yes—
490C2×C4C23×C4×C1111yescharacteristic
491C2×C4C22×D4×C1111yescharacteristic
492C2×C4C2×C11×#4111yescharacteristic
493C2×C4C2×C11×#4111yescharacteristic
494C2×C4C11×H(5,𝔽2)11yescharacteristic
495C2×C4C11×2−1+411yescharacteristic
496C8—22no—
497C8—42no—
498C8—41no—
499C22—24no—
500C22—24no—
501C22—24no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—42no—
506C22—42no—
507C22—42no—
508C22—42no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22C22×C11×C22⋊C411yescharacteristic
514C22C11×#54611yescharacteristic
515C22C11×#54711yescharacteristic
516C22C2×C11×#13511yescharacteristic
517C22C2×C11×#13511yescharacteristic
518C22C11×#57611yescharacteristic
519C22C11×#57711yescharacteristic
520C4—22no—
521C4—24no—
522C4—42no—
523C4—44no—
524C4—42no—
525C4—82no—
526C4—81no—
527C4C11×#41614yes—
528C4C4×C11×#4111yescharacteristic
529C4C11×#52011yescharacteristic
530C4C11×#54611yescharacteristic
531C4C11×#54711yescharacteristic
532C2—44no—
533C2—82no—
534C2C11×#233911yescharacteristic
535C2C2×C11×#41611yescharacteristic
536C2C11×#289711yescharacteristic
537C2C11×#330311yescharacteristic
538C2C11×#330511yescharacteristic
539C2C11×#334011yescharacteristic
540C2C11×#334111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#555C2
LCSG ▷ C2×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×C8×D4×C11C2semidirect
3. C11×#2354C2semidirect
4. C11×#1990C2semidirect
5. C11×#1987C2semidirect
6. C11×#1893C2semidirect
7. C11×#1875C2semidirect
8. C11×#1825C2semidirect
9. C11×#1802C2semidirect
10. C4×C11×#102C2semidirect
11. C11×#1735C2semidirect
14. C11×#555C4semidirect
98. #22489C11direct (N × H)
170. C2×C8×D4C2×C11semidirect
171. #2354C2×C11semidirect
172. #1990C2×C11semidirect
173. #1987C2×C11semidirect
174. #1893C2×C11semidirect
175. #1875C2×C11semidirect
176. #1825C2×C11semidirect
177. #1802C2×C11semidirect
178. C4×#102C2×C11semidirect
179. #1735C2×C11semidirect
242. #555C4×C11semidirect
438. C11#22489direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5552
C2×C8×D4×C112
C11×#23542
C11×#19902
C11×#19872
C11×#18932
C11×#18752
C11×#18252
C11×#18022
C4×C11×#1022
C11×#17352
#2248911