Finite Group Databasebeta

← C11×#25011 #14602204

Subgroups — C11×#25011 #14602204

Order 2816.

910 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#482C212yesmaximal, complemented
2C11×#2537C211yesmaximal, characteristic
3C11×#2354C211yesmaximal, characteristic, complemented
4C11×#2076C212yesmaximal, complemented
5C11×#2033C212yesmaximal, complemented
6C11×#1954C211yesmaximal, characteristic, complemented
7C11×#1948C211yesmaximal, characteristic, complemented
8C11×#1854C212yesmaximal, complemented
9C11×#1845C211yesmaximal, characteristic, complemented
10C11×#1802C211yesmaximal, characteristic, complemented
11C4×C11×#102C211yesmaximal, characteristic, complemented
12C2×C11×#121—21no—
13C2×C11×#121C2212yes—
14C2×C4×D4×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×C11×#117C2212yes—
17C11×#482—28no—
18C2×C11×#107C2212yes—
19C2×C11×#107C2212yes—
20C2×C11×#106C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2212yes—
24C2×C11×#102C2211yescharacteristic
25C2×C11×C22⋊C8C2212yes—
26C2×C11×C22⋊C8C2212yes—
27C2×C4×C8×C11C2211yescharacteristic
28C11×#394—22no—
29C11×#390—21no—
30C11×#388—22no—
31C11×#384C2211yescharacteristic
32C11×#384C2211yescharacteristic
33C11×#380—21no—
34C11×#380C2212yes—
35C11×#380C2212yes—
36C4×C11×C4⋊C4—21no—
37C4×C11×C4⋊C4C2211yescharacteristic
38C11×#340C2212yes—
39C11×#340C2211yescharacteristic
40C11×#340C2211yescharacteristic
41C11×#340C2212yes—
42C22×D4×C11—22no—
43C22×D4×C11D411yescharacteristic
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C23×C4×C11C2312yes—
47C22×C8×C11C2312yes—
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C11×#121—24no—
51C11×#121—42no—
52C11×#121—44no—
53C4×D4×C11—22no—
54C4×D4×C11—22no—
55C4×D4×C11—22no—
56C4×D4×C11—22no—
57C11×#117—24no—
58C11×#117—42no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4D412yes—
75C2×C42×C11—22no—
76C2×C42×C11—21no—
77C2×C42×C11C2311yescharacteristic
78C11×#107—24no—
79C11×#107—42no—
80C11×#106—24no—
81C11×C4⋊C8—22no—
82C11×#102—24no—
83C11×#102—22no—
84C11×#102D414yescomplemented
85C11×C22⋊C8—24no—
86C11×C22⋊C8—24no—
87C4×C8×C11—22no—
88C11×#95—22no—
89C11×#95—21no—
90C11×#95—22no—
91#25011C1111yesmaximal, characteristic, direct product factor, Sylow
92C24×C11—21no—
93C24×C11C2×D412yes—
94C2×D4×C11—22no—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—44no—
103C2×D4×C11—44no—
104C2×D4×C11—82no—
105C2×D4×C11C2×D412yes—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C2×C8×C11—22no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11C2×D412yes—
132C2×C8×C11#4112yes—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—42no—
144C11×C4⋊C4—42no—
145C11×C4⋊C4—81no—
146C11×C4⋊C4—81no—
147C11×C4⋊C4C2×D412yes—
148C11×C22⋊C4—24no—
149C11×C22⋊C4—44no—
150C11×C22⋊C4—44no—
151C11×C22⋊C4—44no—
152C11×C22⋊C4—42no—
153C11×C22⋊C4—82no—
154C42×C11—44no—
155C42×C11—42no—
156C42×C11#4112yes—
157C42×C11#4112yes—
158C2×#482C2×C1112yescomplemented
159#2537C2×C1111yescharacteristic
160#2354C2×C1111yescharacteristic, complemented
161#2076C2×C1112yescomplemented
162#2033C2×C1112yescomplemented
163#1954C2×C1111yescharacteristic, complemented
164#1948C2×C1111yescharacteristic, complemented
165#1854C2×C1112yescomplemented
166#1845C2×C1111yescharacteristic, complemented
167#1802C2×C1111yescharacteristic, complemented
168C4×#102C2×C1111yescharacteristic, complemented
169C23×C11—22no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—22no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11C22×D411yescharacteristic
184D4×C11—22no—
185D4×C11—22no—
186D4×C11—41no—
187D4×C11—41no—
188D4×C11—44no—
189D4×C11—88no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—41no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—84no—
215C2×C4×C11#12312yes—
216C2×C4×C11#12312yes—
217C2×C4×C11#13512yes—
218C2×C4×C11AGL(1,ℤ/8)12yes—
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C2×C4×C11H(5,𝔽2)11yescharacteristic
224C2×C4×C112−1+411yescharacteristic
225C8×C11—22no—
226C8×C11—22no—
227C8×C11—42no—
228C2×#121—21no—
229C2×#121C22×C1112yes—
230C2×C4×D4C22×C1111yescharacteristic
231C2×C4×D4C22×C1111yescharacteristic
232C2×#117C22×C1112yes—
233#482—28no—
234C2×#107C22×C1112yes—
235C2×#107C22×C1112yes—
236C2×#106C22×C1112yes—
237C2×C4⋊C8C22×C1111yescharacteristic
238C2×#102C22×C1112yes—
239C2×#102C22×C1111yescharacteristic
240C2×#102C22×C1111yescharacteristic
241C2×C22⋊C8C22×C1112yes—
242C2×C22⋊C8C22×C1112yes—
243C2×C4×C8C22×C1111yescharacteristic
244#394—22no—
245#390—21no—
246#388—22no—
247#384C22×C1111yescharacteristic
248#384C22×C1111yescharacteristic
249#380—21no—
250#380C22×C1112yes—
251#380C22×C1112yes—
252C4×C4⋊C4—21no—
253C4×C4⋊C4C22×C1111yescharacteristic
254#340C22×C1112yes—
255#340C22×C1111yescharacteristic
256#340C22×C1112yes—
257#340C22×C1111yescharacteristic
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—42no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—81no—
269C22×C11—81no—
270C22×C11—81no—
271C22×C11—81no—
272C22×C11C2×#12311yescharacteristic
273C22×C11D4211yescharacteristic
274C22×C11#54711yescharacteristic
275C22×C11C2×#13511yescharacteristic
276C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
277C22×C11#57611yescharacteristic
278C22×C11#57811yescharacteristic
279C4×C11—22no—
280C4×C11—42no—
281C4×C11—42no—
282C4×C11—81no—
283C4×C11—81no—
284C4×C11—82no—
285C4×C11—82no—
286C4×C11#48214yescomplemented
287C4×C11#53211yescharacteristic
288C4×C11#54211yescharacteristic
289C4×C11#54711yescharacteristic
290C4×C11#55311yescharacteristic
291C22×D4—22no—
292C22×D4D4×C1111yescharacteristic
293C22×D4C23×C1111yescharacteristic
294C23×C4—21no—
295C23×C4C23×C1112yes—
296C22×C8C23×C1112yes—
297C22×C8C23×C1111yescharacteristic
298C22×C8C23×C1111yescharacteristic
299#121—24no—
300#121—42no—
301#121—44no—
302C4×D4—22no—
303C4×D4—22no—
304C4×D4—22no—
305C4×D4—22no—
306#117—24no—
307#117—42no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4D4×C1111yescharacteristic
313C2×C4⋊C4C23×C1112yes—
314C2×C4⋊C4C23×C1111yescharacteristic
315C2×C4⋊C4C23×C1112yes—
316C2×C4⋊C4C23×C1111yescharacteristic
317C2×C4⋊C4C23×C1111yescharacteristic
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—22no—
325C2×C42—21no—
326C2×C42C23×C1111yescharacteristic
327#107—24no—
328#107—42no—
329#106—24no—
330C4⋊C8—22no—
331#102—24no—
332#102—22no—
333#102D4×C1114yescomplemented
334C22⋊C8—24no—
335C22⋊C8—24no—
336C4×C8—22no—
337#95—22no—
338#95—21no—
339#95—22no—
340C2×C11—82no—
341C2×C11—82no—
342C2×C11#242211yescharacteristic
343C2×C11C2×#48211yescharacteristic
344C2×C11#309811yescharacteristic
345C2×C11#327411yescharacteristic
346C2×C11#328311yescharacteristic
347C2×C11#334111yescharacteristic
348C2×C11#335311yescharacteristic
349C24—21no—
350C24C2×D4×C1112yes—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—22no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—44no—
360C2×D4—44no—
361C2×D4—82no—
362C2×D4C2×D4×C1112yes—
363C22×C4—21no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4C2×D4×C1112yes—
378C22×C4C2×D4×C1111yescharacteristic
379C22×C4C2×D4×C1111yescharacteristic
380C22×C4C24×C1111yescharacteristic
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8C2×D4×C1112yes—
389C2×C8C11×#4112yes—
390C4⋊C4—22no—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—21no—
400C4⋊C4—42no—
401C4⋊C4—42no—
402C4⋊C4—81no—
403C4⋊C4—81no—
404C4⋊C4C2×D4×C1112yes—
405C22⋊C4—24no—
406C22⋊C4—44no—
407C22⋊C4—44no—
408C22⋊C4—44no—
409C22⋊C4—42no—
410C22⋊C4—82no—
411C42—44no—
412C42—42no—
413C42C11×#4112yes—
414C42C11×#4112yes—
415C11#2501111yescharacteristic, direct product factor, Sylow
416C23—22no—
417C23—22no—
418C23—22no—
419C23—22no—
420C23—22no—
421C23—22no—
422C23—22no—
423C23—22no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23C22×D4×C1111yescharacteristic
431D4—22no—
432D4—22no—
433D4—41no—
434D4—41no—
435D4—44no—
436D4—88no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—84no—
462C2×C4C11×#12312yes—
463C2×C4C11×#12312yes—
464C2×C4C11×#13512yes—
465C2×C4C11×AGL(1,ℤ/8)12yes—
466C2×C4C22×D4×C1111yescharacteristic
467C2×C4C2×C11×#4111yescharacteristic
468C2×C4C2×C11×#4111yescharacteristic
469C2×C4C2×C11×#4111yescharacteristic
470C2×C4C11×H(5,𝔽2)11yescharacteristic
471C2×C4C11×2−1+411yescharacteristic
472C8—22no—
473C8—22no—
474C8—42no—
475C22—42no—
476C22—42no—
477C22—42no—
478C22—42no—
479C22—42no—
480C22—42no—
481C22—42no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22—81no—
486C22—81no—
487C22—81no—
488C22—81no—
489C22C2×C11×#12311yescharacteristic
490C22D42×C1111yescharacteristic
491C22C11×#54711yescharacteristic
492C22C2×C11×#13511yescharacteristic
493C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
494C22C11×#57611yescharacteristic
495C22C11×#57811yescharacteristic
496C4—22no—
497C4—42no—
498C4—42no—
499C4—82no—
500C4—82no—
501C4—81no—
502C4—81no—
503C4C11×#48214yescomplemented
504C4C11×#53211yescharacteristic
505C4C11×#54211yescharacteristic
506C4C11×#54711yescharacteristic
507C4C11×#55311yescharacteristic
508C2—82no—
509C2—82no—
510C2C11×#242211yescharacteristic
511C2C2×C11×#48211yescharacteristic
512C2C11×#309811yescharacteristic
513C2C11×#327411yescharacteristic
514C2C11×#328311yescharacteristic
515C2C11×#334111yescharacteristic
516C2C11×#335311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2537C2
LCSG ▷ C22×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
1. C2×C11×#482C2semidirect
3. C11×#2354C2semidirect
4. C11×#2076C2semidirect
5. C11×#2033C2semidirect
6. C11×#1954C2semidirect
7. C11×#1948C2semidirect
8. C11×#1854C2semidirect
9. C11×#1845C2semidirect
10. C11×#1802C2semidirect
11. C4×C11×#102C2semidirect
84. C11×#102D4semidirect
91. #25011C11direct (N × H)
158. C2×#482C2×C11semidirect
160. #2354C2×C11semidirect
161. #2076C2×C11semidirect
162. #2033C2×C11semidirect
163. #1954C2×C11semidirect
164. #1948C2×C11semidirect
165. #1854C2×C11semidirect
166. #1845C2×C11semidirect
167. #1802C2×C11semidirect
168. C4×#102C2×C11semidirect
286. C4×C11#482semidirect
333. #102D4×C11semidirect
415. C11#25011direct (N × H)
503. C4C11×#482semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4822
C11×#25372
C11×#23542
C11×#20762
C11×#20332
C11×#19542
C11×#19482
C11×#18542
C11×#18452
C11×#18022
C4×C11×#1022
#2501111