Finite Group Databasebeta

← C11×#23307 #14600500

Subgroups — C11×#23307 #14600500

Order 2816.

1052 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C11×#120C211yesmaximal, characteristic
2C11×#1955C212yesmaximal, complemented
3C11×#1954C211yesmaximal, characteristic, complemented
4C11×#1924C212yesmaximal, complemented
5C11×#1924C212yesmaximal, complemented
6C11×#1923C212yesmaximal, complemented
7C11×#1869C211yesmaximal, characteristic, complemented
8C11×#1869C212yesmaximal, complemented
9C11×#1779C212yesmaximal, complemented
10C24×C4×C11C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic, complemented
12C2×C11×#120C411yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C2×C4×D4×C11C2212yes—
15C2×C11×C4⋊C8C2212yescomplemented
16C2×C11×C4⋊C8C2211yescharacteristic, complemented
17C2×C11×C22⋊C8C2212yes—
18C2×C11×C22⋊C8C2212yes—
19C2×C11×C22⋊C8C2212yes—
20C2×C11×C22⋊C8C2212yes—
21C2×C11×C22⋊C8C2212yes—
22C2×C11×C22⋊C8C2212yes—
23C2×C11×C22⋊C8C2212yescomplemented
24C2×C11×C22⋊C8C2211yescharacteristic, complemented
25C2×C11×#97C2212yescomplemented
26C2×C4×C8×C11C2211yescharacteristic, complemented
27C11×#386C412yes—
28C11×#386C411yescharacteristic
29C11×#385C411yescharacteristic
30C11×#385C412yes—
31C11×#379C411yescharacteristic
32C4×C11×C22⋊C4C2212yes—
33C4×C11×C22⋊C4C2211yescharacteristic
34C11×#336C2212yescomplemented
35C11×#336C2212yescomplemented
36C11×#336C2212yescomplemented
37C25×C11C2×C411yescharacteristic
38C22×D4×C11C2×C412yes—
39C22×D4×C11C2×C411yescharacteristic
40C23×C4×C11—41no—
41C23×C4×C11—42no—
42C23×C4×C11—41no—
43C23×C4×C11—42no—
44C23×C4×C11C2×C411yescharacteristic
45C23×C4×C11C2×C412yes—
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2312yes—
48C23×C4×C11C2311yescharacteristic
49C22×C8×C11—41no—
50C22×C8×C11—42no—
51C22×C8×C11C2312yes—
52C22×C8×C11C2312yes—
53C22×C8×C11C2312yes—
54C22×C8×C11C2312yes—
55C11×#120—24no—
56C4×D4×C11—41no—
57C4×D4×C11—42no—
58C4×D4×C11—41no—
59C4×D4×C11—42no—
60C2×C11×C4⋊C4C2×C412yes—
61C2×C11×C4⋊C4C2×C411yescharacteristic
62C2×C11×C22⋊C4C2×C412yes—
63C2×C11×C22⋊C4C2×C411yescharacteristic
64C2×C11×C22⋊C4C2×C412yes—
65C2×C11×C22⋊C4C2×C411yescharacteristic
66C2×C11×C22⋊C4C2×C411yescharacteristic
67C2×C11×C22⋊C4C2×C412yes—
68C2×C11×C22⋊C4C2×C411yescharacteristic
69C2×C11×C22⋊C4C2×C412yes—
70C2×C42×C11C2311yescharacteristic
71C2×C42×C11C2312yes—
72C11×C4⋊C8—42no—
73C11×C4⋊C8—41no—
74C11×C22⋊C8—42no—
75C11×C22⋊C8—42no—
76C11×C22⋊C8—42no—
77C11×C22⋊C8—42no—
78C11×C22⋊C8—42no—
79C11×C22⋊C8—42no—
80C11×C22⋊C8—42no—
81C11×C22⋊C8—41no—
82C11×#97—42no—
83C4×C8×C11—41no—
84C11×#95C2×C412yes—
85C11×#95C2×C412yes—
86C11×#95C2×C412yes—
87#23307C1111yesmaximal, characteristic, direct product factor, Sylow
88C24×C11—22no—
89C24×C11—24no—
90C24×C11—41no—
91C24×C11—42no—
92C24×C11—41no—
93C24×C11C22×C411yescharacteristic
94C24×C11C22×C411yescharacteristic
95C24×C11C22×C412yes—
96C2×D4×C11—24no—
97C2×D4×C11—24no—
98C2×D4×C11—41no—
99C2×D4×C11—42no—
100C2×D4×C11—41no—
101C2×D4×C11M1614yes—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—42no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11—41no—
120C22×C4×C11—42no—
121C22×C4×C11—44no—
122C22×C4×C11—48no—
123C22×C4×C11—44no—
124C22×C4×C11C22×C411yescharacteristic
125C22×C4×C11C22×C412yes—
126C22×C4×C11C22×C412yes—
127C22×C4×C11C22×C411yescharacteristic
128C22×C4×C11C22×C412yes—
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11—44no—
145C11×C4⋊C4—41no—
146C11×C4⋊C4—42no—
147C11×C22⋊C4—22no—
148C11×C22⋊C4—24no—
149C11×C22⋊C4—24no—
150C11×C22⋊C4—41no—
151C11×C22⋊C4—42no—
152C11×C22⋊C4—41no—
153C11×C22⋊C4—42no—
154C11×C22⋊C4—41no—
155C42×C11—21no—
156C42×C11—22no—
157C42×C11—21no—
158C42×C11—22no—
159C4×#120C2×C1111yescharacteristic
160#1955C2×C1112yescomplemented
161#1954C2×C1111yescharacteristic, complemented
162#1924C2×C1112yescomplemented
163#1924C2×C1112yescomplemented
164#1923C2×C1112yescomplemented
165#1869C2×C1111yescharacteristic, complemented
166#1869C2×C1112yescomplemented
167#1779C2×C1112yescomplemented
168C23×C11—21no—
169C23×C11—22no—
170C23×C11—21no—
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—22no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—21no—
180C23×C11—21no—
181C23×C11—22no—
182C23×C11—48no—
183C23×C11—44no—
184C23×C11—44no—
185C23×C11—48no—
186C23×C11—44no—
187C23×C11C2×M1612yes—
188C23×C11C2×M1612yes—
189C23×C11#13114yes—
190C23×C11C23×C411yescharacteristic
191D4×C11—44no—
192D4×C11—48no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—22no—
196C2×C4×C11—21no—
197C2×C4×C11—22no—
198C2×C4×C11—21no—
199C2×C4×C11—22no—
200C2×C4×C11—21no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
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—48no—
211C2×C4×C11—44no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—42no—
222C2×C4×C11C2×M1612yes—
223C2×C4×C11H(5,𝔽2)11yescharacteristic
224C2×C4×C11H(5,𝔽2)12yes—
225C2×C4×C11H(5,𝔽2)11yescharacteristic
226C2×C4×C11H(5,𝔽2)12yes—
227C8×C11—42no—
228C8×C11—42no—
229C8×C11—42no—
230C8×C11—42no—
231C24×C4C22×C1111yescharacteristic
232C23×C8C22×C1111yescharacteristic, complemented
233C2×#120C4×C1111yescharacteristic
234C2×C4×D4C22×C1111yescharacteristic
235C2×C4×D4C22×C1112yes—
236C2×C4⋊C8C22×C1112yescomplemented
237C2×C4⋊C8C22×C1111yescharacteristic, complemented
238C2×C22⋊C8C22×C1112yes—
239C2×C22⋊C8C22×C1112yes—
240C2×C22⋊C8C22×C1112yes—
241C2×C22⋊C8C22×C1112yes—
242C2×C22⋊C8C22×C1112yes—
243C2×C22⋊C8C22×C1112yes—
244C2×C22⋊C8C22×C1112yescomplemented
245C2×C22⋊C8C22×C1111yescharacteristic, complemented
246C2×#97C22×C1112yescomplemented
247C2×C4×C8C22×C1111yescharacteristic, complemented
248#386C4×C1112yes—
249#386C4×C1111yescharacteristic
250#385C4×C1111yescharacteristic
251#385C4×C1112yes—
252#379C4×C1111yescharacteristic
253C4×C22⋊C4C22×C1112yes—
254C4×C22⋊C4C22×C1111yescharacteristic
255#336C22×C1112yescomplemented
256#336C22×C1112yescomplemented
257#336C22×C1112yescomplemented
258C22×C11—22no—
259C22×C11—22no—
260C22×C11—24no—
261C22×C11—24no—
262C22×C11—24no—
263C22×C11—24no—
264C22×C11—24no—
265C22×C11—416no—
266C22×C11—41no—
267C22×C11—42no—
268C22×C11—41no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—42no—
274C22×C11—41no—
275C22×C11—41no—
276C22×C11#51811yescharacteristic
277C22×C11#51812yes—
278C22×C11C22×M1611yescharacteristic
279C22×C11C2×#13112yes—
280C22×C11#56811yescharacteristic
281C4×C11—22no—
282C4×C11—41no—
283C4×C11—41no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11—42no—
287C4×C11—41no—
288C4×C11#56012yes—
289C4×C11#56011yescharacteristic
290C4×C11H(3,𝔽4)11yescharacteristic
291C25C2×C4×C1111yescharacteristic
292C22×D4C2×C4×C1112yes—
293C22×D4C2×C4×C1111yescharacteristic
294C23×C4—41no—
295C23×C4—42no—
296C23×C4—41no—
297C23×C4—42no—
298C23×C4C2×C4×C1111yescharacteristic
299C23×C4C2×C4×C1112yes—
300C23×C4C23×C1111yescharacteristic
301C23×C4C23×C1111yescharacteristic
302C23×C4C23×C1112yes—
303C22×C8—41no—
304C22×C8—42no—
305C22×C8C23×C1112yes—
306C22×C8C23×C1112yes—
307C22×C8C23×C1112yes—
308C22×C8C23×C1112yes—
309#120—24no—
310C4×D4—41no—
311C4×D4—42no—
312C4×D4—41no—
313C4×D4—42no—
314C2×C4⋊C4C2×C4×C1112yes—
315C2×C4⋊C4C2×C4×C1111yescharacteristic
316C2×C22⋊C4C2×C4×C1111yescharacteristic
317C2×C22⋊C4C2×C4×C1112yes—
318C2×C22⋊C4C2×C4×C1112yes—
319C2×C22⋊C4C2×C4×C1111yescharacteristic
320C2×C22⋊C4C2×C4×C1112yes—
321C2×C22⋊C4C2×C4×C1111yescharacteristic
322C2×C22⋊C4C2×C4×C1112yes—
323C2×C22⋊C4C2×C4×C1111yescharacteristic
324C2×C42C23×C1111yescharacteristic
325C2×C42C23×C1112yes—
326C4⋊C8—42no—
327C4⋊C8—41no—
328C22⋊C8—42no—
329C22⋊C8—42no—
330C22⋊C8—42no—
331C22⋊C8—42no—
332C22⋊C8—42no—
333C22⋊C8—42no—
334C22⋊C8—42no—
335C22⋊C8—41no—
336#97—42no—
337C4×C8—41no—
338#95C2×C4×C1112yes—
339#95C2×C4×C1112yes—
340#95C2×C4×C1112yes—
341C2×C11—42no—
342C2×C11—42no—
343C2×C11—44no—
344C2×C11#237511yescharacteristic
345C2×C11#297311yescharacteristic
346C2×C11#297412yes—
347C2×C11#297612yes—
348C2×C11#297711yescharacteristic
349C24—22no—
350C24—24no—
351C24—41no—
352C24—42no—
353C24—41no—
354C24C22×C4×C1111yescharacteristic
355C24C22×C4×C1111yescharacteristic
356C24C22×C4×C1112yes—
357C2×D4—24no—
358C2×D4—24no—
359C2×D4—41no—
360C2×D4—42no—
361C2×D4—41no—
362C2×D4C11×M1614yes—
363C22×C4—21no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—41no—
381C22×C4—42no—
382C22×C4—44no—
383C22×C4—48no—
384C22×C4—44no—
385C22×C4C22×C4×C1111yescharacteristic
386C22×C4C22×C4×C1112yes—
387C22×C4C22×C4×C1112yes—
388C22×C4C22×C4×C1111yescharacteristic
389C22×C4C22×C4×C1112yes—
390C22×C4C22×C4×C1111yescharacteristic
391C22×C4C22×C4×C1111yescharacteristic
392C22×C4C24×C1111yescharacteristic
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—22no—
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—22no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—44no—
406C4⋊C4—41no—
407C4⋊C4—42no—
408C22⋊C4—22no—
409C22⋊C4—24no—
410C22⋊C4—24no—
411C22⋊C4—42no—
412C22⋊C4—41no—
413C22⋊C4—42no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C42—21no—
417C42—22no—
418C42—21no—
419C42—22no—
420C11#2330711yescharacteristic, direct product factor, Sylow
421C23—21no—
422C23—22no—
423C23—21no—
424C23—22no—
425C23—22no—
426C23—22no—
427C23—22no—
428C23—22no—
429C23—22no—
430C23—22no—
431C23—22no—
432C23—21no—
433C23—21no—
434C23—22no—
435C23—48no—
436C23—44no—
437C23—44no—
438C23—48no—
439C23—44no—
440C23C2×C11×M1612yes—
441C23C2×C11×M1612yes—
442C23C11×#13114yes—
443C23C23×C4×C1111yescharacteristic
444D4—44no—
445D4—48no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—22no—
449C2×C4—21no—
450C2×C4—22no—
451C2×C4—21no—
452C2×C4—22no—
453C2×C4—21no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—48no—
464C2×C4—44no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4C2×C11×M1612yes—
476C2×C4C11×H(5,𝔽2)11yescharacteristic
477C2×C4C11×H(5,𝔽2)12yes—
478C2×C4C11×H(5,𝔽2)11yescharacteristic
479C2×C4C11×H(5,𝔽2)12yes—
480C8—42no—
481C8—42no—
482C8—42no—
483C8—42no—
484C22—22no—
485C22—22no—
486C22—24no—
487C22—24no—
488C22—24no—
489C22—24no—
490C22—24no—
491C22—416no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—42no—
501C22—41no—
502C22C11×#51811yescharacteristic
503C22C11×#51812yes—
504C22C22×C11×M1611yescharacteristic
505C22C2×C11×#13112yes—
506C22C11×#56811yescharacteristic
507C4—22no—
508C4—42no—
509C4—42no—
510C4—41no—
511C4—41no—
512C4—42no—
513C4—41no—
514C4C11×#56012yes—
515C4C11×#56011yescharacteristic
516C4C11×H(3,𝔽4)11yescharacteristic
517C2—42no—
518C2—44no—
519C2—42no—
520C2C11×#237511yescharacteristic
521C2C11×#297311yescharacteristic
522C2C11×#297412yes—
523C2C11×#297612yes—
524C2C11×#297711yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC2×C11×#120C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1955C2semidirect
3. C11×#1954C2semidirect
4. C11×#1924C2semidirect
5. C11×#1924C2semidirect
6. C11×#1923C2semidirect
7. C11×#1869C2semidirect
8. C11×#1869C2semidirect
9. C11×#1779C2semidirect
11. C23×C8×C11C22semidirect
15. C2×C11×C4⋊C8C22semidirect
16. C2×C11×C4⋊C8C22semidirect
23. C2×C11×C22⋊C8C22semidirect
24. C2×C11×C22⋊C8C22semidirect
25. C2×C11×#97C22semidirect
26. C2×C4×C8×C11C22semidirect
34. C11×#336C22semidirect
35. C11×#336C22semidirect
36. C11×#336C22semidirect
87. #23307C11direct (N × H)
160. #1955C2×C11semidirect
161. #1954C2×C11semidirect
162. #1924C2×C11semidirect
163. #1924C2×C11semidirect
164. #1923C2×C11semidirect
165. #1869C2×C11semidirect
166. #1869C2×C11semidirect
167. #1779C2×C11semidirect
232. C23×C8C22×C11semidirect
236. C2×C4⋊C8C22×C11semidirect
237. C2×C4⋊C8C22×C11semidirect
244. C2×C22⋊C8C22×C11semidirect
245. C2×C22⋊C8C22×C11semidirect
246. C2×#97C22×C11semidirect
247. C2×C4×C8C22×C11semidirect
255. #336C22×C11semidirect
256. #336C22×C11semidirect
257. #336C22×C11semidirect
420. C11#23307direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C11×#1202
C11×#19552
C11×#19542
C11×#19242
C11×#19232
C11×#18692
C11×#17792
#2330711