Finite Group Databasebeta

← C11×#21887 #14599080

Subgroups — C11×#21887 #14599080

Order 2816.

1194 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#529C211yesmaximal, characteristic
2C22×C11×C4⋊C8C211yesmaximal, characteristic, complemented
3C11×#2285C211yesmaximal, characteristic, complemented
4C11×#1989C212yesmaximal, complemented
5C11×#1983C212yesmaximal, complemented
6C11×#1893C212yesmaximal
7C11×#1892C212yesmaximal, complemented
8C11×#1803C212yesmaximal, complemented
9C11×#1802C212yesmaximal, complemented
10C23×C8×C11C2212yes—
11C11×#529—24no—
12C11×#529C418yescomplemented
13C2×C11×#126—21no—
14C2×C11×#125C2211yescharacteristic
15C2×C11×#124C2211yescharacteristic
16C2×C11×#123—21no—
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C2×C11×#117—21no—
23C2×C11×#117—21no—
24C22×C42×C11C2211yescharacteristic
25C2×C11×C4⋊C8—24no—
26C2×C11×C4⋊C8C2212yes—
27C2×C11×C4⋊C8C2212yes—
28C2×C11×#103C2214yes—
29C2×C11×#102C2214yes—
30C11×#384C2212yes—
31C11×#382—21no—
32C11×#380—21no—
33C11×#380C2212yes—
34C4×C11×C4⋊C4—21no—
35C4×C11×C4⋊C4C2212yes—
36C11×#340C2214yes—
37C11×#340C2214yes—
38C22×Q8×C11C2311yescharacteristic
39C22×D4×C11—21no—
40C22×D4×C11C2311yescharacteristic
41C23×C4×C11—21no—
42C23×C4×C11D411yescharacteristic
43C23×C4×C11D411yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C22×C8×C11—24no—
46C22×C8×C11—44no—
47C22×C8×C11C2314yes—
48C11×#126—28no—
49C11×#125—22no—
50C11×#125C2×C414yes—
51C11×#124—22no—
52C11×#124C2×C414yes—
53C11×#123—28no—
54C11×C22⋊Q8—22no—
55C11×C22⋊Q8C2×C414yes—
56C11×#121—22no—
57C11×#121C2×C414yes—
58C4×Q8×C11—22no—
59C4×Q8×C11C2×C414yes—
60C4×D4×C11—28no—
61C4×D4×C11—22no—
62C4×D4×C11C2×C414yes—
63C11×#117—28no—
64C11×#117—44no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4C2314yes—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—22no—
80C2×C42×C11—21no—
81C2×C42×C11—22no—
82C2×C42×C11C2×C414yes—
83C2×C42×C11D411yescharacteristic
84C2×C42×C11D411yescharacteristic
85C2×C42×C11D414yes—
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C11×C4⋊C8—24no—
89C11×C4⋊C8—24no—
90C11×#103—44no—
91C11×#102—44no—
92C11×#95—22no—
93C11×#95—22no—
94#21887C1111yesmaximal, characteristic, direct product factor, Sylow
95C24×C11—21no—
96C24×C11C2×D411yescharacteristic
97C2×Q8×C11—21no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11C22×C412yes—
101C2×D4×C11—24no—
102C2×D4×C11—21no—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—42no—
106C2×D4×C11—42no—
107C2×D4×C11C22×C412yes—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—24no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—24no—
117C22×C4×C11—24no—
118C22×C4×C11—44no—
119C22×C4×C11C22⋊C414yes—
120C22×C4×C11C22⋊C414yes—
121C22×C4×C11C22×C412yes—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C2×C8×C11—24no—
130C2×C8×C11—24no—
131C2×C8×C11—24no—
132C2×C8×C11—48no—
133C11×C4⋊C4—24no—
134C11×C4⋊C4—24no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—44no—
142C11×C4⋊C4—44no—
143C11×C4⋊C4C22×C412yes—
144C11×C4⋊C4C22×C412yes—
145C11×C22⋊C4—24no—
146C11×C22⋊C4—24no—
147C11×C22⋊C4—24no—
148C11×C22⋊C4—24no—
149C11×C22⋊C4—24no—
150C11×C22⋊C4—44no—
151C42×C11—24no—
152C42×C11—44no—
153C42×C11C22⋊C414yes—
154C42×C11C22⋊C414yes—
155C42×C11C22×C412yes—
156C42×C11C22×C412yes—
157C42×C11C2×D412yes—
158C42×C11C2×D412yes—
159C2×#529C2×C1111yescharacteristic
160C22×C4⋊C8C2×C1111yescharacteristic, complemented
161#2285C2×C1111yescharacteristic, complemented
162#1989C2×C1112yescomplemented
163#1983C2×C1112yescomplemented
164#1893C2×C1112yes—
165#1892C2×C1112yescomplemented
166#1803C2×C1112yescomplemented
167#1802C2×C1112yescomplemented
168C23×C11—22no—
169C23×C11—22no—
170C23×C11—22no—
171C23×C11—42no—
172C23×C11—42no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11C2×C22⋊C412yes—
176C23×C11AGL(1,ℤ/8)12yes—
177C23×C11#13712yes—
178C23×C11C22×D411yescharacteristic
179Q8×C11—24no—
180Q8×C11—41no—
181Q8×C11—41no—
182D4×C11—24no—
183D4×C11—48no—
184D4×C11—41no—
185D4×C11—41no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—28no—
193C2×C4×C11—24no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—28no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—48no—
205C2×C4×C11—44no—
206C2×C4×C11—44no—
207C2×C4×C11—44no—
208C2×C4×C11C2×C22⋊C412yes—
209C2×C4×C11C2×C22⋊C412yes—
210C2×C4×C11C2×C22⋊C412yes—
211C2×C4×C11C2×C22⋊C412yes—
212C2×C4×C11C2×C22⋊C412yes—
213C2×C4×C11#13514yes—
214C2×C4×C11C23×C411yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11H(5,𝔽2)12yes—
217C2×C4×C112−1+412yes—
218C8×C11—44no—
219C23×C8C22×C1112yes—
220#529—24no—
221#529C4×C1118yescomplemented
222C2×#126—21no—
223C2×#125C22×C1111yescharacteristic
224C2×#124C22×C1111yescharacteristic
225C2×#123—21no—
226C2×C22⋊Q8C22×C1111yescharacteristic
227C2×#121C22×C1111yescharacteristic
228C2×C4×Q8C22×C1111yescharacteristic
229C2×C4×D4—21no—
230C2×C4×D4C22×C1111yescharacteristic
231C2×#117—21no—
232C2×#117—21no—
233C22×C42C22×C1111yescharacteristic
234C2×C4⋊C8—24no—
235C2×C4⋊C8C22×C1112yes—
236C2×C4⋊C8C22×C1112yes—
237C2×#103C22×C1114yes—
238C2×#102C22×C1114yes—
239#384C22×C1112yes—
240#382—21no—
241#380—21no—
242#380C22×C1112yes—
243C4×C4⋊C4—21no—
244C4×C4⋊C4C22×C1112yes—
245#340C22×C1114yes—
246#340C22×C1114yes—
247C22×C11—22no—
248C22×C11—22no—
249C22×C11—24no—
250C22×C11—24no—
251C22×C11—42no—
252C22×C11—42no—
253C22×C11—42no—
254C22×C11—82no—
255C22×C11—82no—
256C22×C11#41714yes—
257C22×C11C22×C22⋊C411yescharacteristic
258C22×C11#53712yes—
259C22×C11C2×#13512yes—
260C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
261C22×C11C2×#13711yescharacteristic
262C4×C11—22no—
263C4×C11—22no—
264C4×C11—22no—
265C4×C11—22no—
266C4×C11—42no—
267C4×C11—42no—
268C4×C11—42no—
269C4×C11—84no—
270C4×C11#41614yes—
271C4×C11#52012yes—
272C4×C11#53511yescharacteristic
273C4×C11#53611yescharacteristic
274C22×Q8C23×C1111yescharacteristic
275C22×D4—21no—
276C22×D4C23×C1111yescharacteristic
277C23×C4—21no—
278C23×C4D4×C1111yescharacteristic
279C23×C4D4×C1111yescharacteristic
280C23×C4C23×C1111yescharacteristic
281C22×C8—24no—
282C22×C8—44no—
283C22×C8C23×C1114yes—
284#126—28no—
285#125—22no—
286#125C2×C4×C1114yes—
287#124—22no—
288#124C2×C4×C1114yes—
289#123—28no—
290C22⋊Q8—22no—
291C22⋊Q8C2×C4×C1114yes—
292#121—22no—
293#121C2×C4×C1114yes—
294C4×Q8—22no—
295C4×Q8C2×C4×C1114yes—
296C4×D4—28no—
297C4×D4—22no—
298C4×D4C2×C4×C1114yes—
299#117—28no—
300#117—44no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4C23×C1114yes—
308C2×C4⋊C4C23×C1111yescharacteristic
309C2×C4⋊C4C23×C1111yescharacteristic
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—22no—
316C2×C42—21no—
317C2×C42—22no—
318C2×C42C2×C4×C1114yes—
319C2×C42D4×C1111yescharacteristic
320C2×C42D4×C1111yescharacteristic
321C2×C42D4×C1114yes—
322C2×C42C23×C1111yescharacteristic
323C2×C42C23×C1111yescharacteristic
324C4⋊C8—24no—
325C4⋊C8—24no—
326#103—44no—
327#102—44no—
328#95—22no—
329#95—22no—
330C2×C11—24no—
331C2×C11—82no—
332C2×C11#231111yescharacteristic
333C2×C11C2×#41611yescharacteristic
334C2×C11C2×#41711yescharacteristic
335C2×C11#324712yes—
336C2×C11#324812yes—
337C24—21no—
338C24C2×D4×C1111yescharacteristic
339C2×Q8—21no—
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8C22×C4×C1112yes—
343C2×D4—24no—
344C2×D4—21no—
345C2×D4—22no—
346C2×D4—22no—
347C2×D4—42no—
348C2×D4—42no—
349C2×D4C22×C4×C1112yes—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—24no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—24no—
359C22×C4—24no—
360C22×C4—44no—
361C22×C4C11×C22⋊C414yes—
362C22×C4C11×C22⋊C414yes—
363C22×C4C22×C4×C1112yes—
364C22×C4C2×D4×C1111yescharacteristic
365C22×C4C2×D4×C1111yescharacteristic
366C22×C4C2×D4×C1111yescharacteristic
367C22×C4C2×D4×C1111yescharacteristic
368C22×C4C2×D4×C1112yes—
369C22×C4C2×D4×C1111yescharacteristic
370C22×C4C24×C1111yescharacteristic
371C2×C8—24no—
372C2×C8—24no—
373C2×C8—24no—
374C2×C8—48no—
375C4⋊C4—24no—
376C4⋊C4—24no—
377C4⋊C4—24no—
378C4⋊C4—24no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—24no—
382C4⋊C4—24no—
383C4⋊C4—44no—
384C4⋊C4—44no—
385C4⋊C4C22×C4×C1112yes—
386C4⋊C4C22×C4×C1112yes—
387C22⋊C4—24no—
388C22⋊C4—24no—
389C22⋊C4—24no—
390C22⋊C4—24no—
391C22⋊C4—24no—
392C22⋊C4—44no—
393C42—24no—
394C42—44no—
395C42C11×C22⋊C414yes—
396C42C11×C22⋊C414yes—
397C42C22×C4×C1112yes—
398C42C22×C4×C1112yes—
399C42C2×D4×C1112yes—
400C42C2×D4×C1112yes—
401C11#2188711yescharacteristic, direct product factor, Sylow
402C23—22no—
403C23—22no—
404C23—22no—
405C23—42no—
406C23—42no—
407C23—41no—
408C23—41no—
409C23C2×C11×C22⋊C412yes—
410C23C11×AGL(1,ℤ/8)12yes—
411C23C11×#13712yes—
412C23C22×D4×C1111yescharacteristic
413Q8—24no—
414Q8—41no—
415Q8—41no—
416D4—24no—
417D4—48no—
418D4—41no—
419D4—41no—
420C2×C4—22no—
421C2×C4—28no—
422C2×C4—22no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—24no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—28no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—48no—
439C2×C4—44no—
440C2×C4—44no—
441C2×C4—44no—
442C2×C4C2×C11×C22⋊C412yes—
443C2×C4C2×C11×C22⋊C412yes—
444C2×C4C2×C11×C22⋊C412yes—
445C2×C4C2×C11×C22⋊C412yes—
446C2×C4C2×C11×C22⋊C412yes—
447C2×C4C11×#13514yes—
448C2×C4C23×C4×C1111yescharacteristic
449C2×C4C22×D4×C1111yescharacteristic
450C2×C4C11×H(5,𝔽2)12yes—
451C2×C4C11×2−1+412yes—
452C8—44no—
453C22—22no—
454C22—24no—
455C22—24no—
456C22—22no—
457C22—42no—
458C22—42no—
459C22—42no—
460C22—82no—
461C22—82no—
462C22C11×#41714yes—
463C22C22×C11×C22⋊C411yescharacteristic
464C22C11×#53712yes—
465C22C2×C11×#13512yes—
466C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
467C22C2×C11×#13711yescharacteristic
468C4—22no—
469C4—22no—
470C4—22no—
471C4—22no—
472C4—42no—
473C4—42no—
474C4—42no—
475C4—84no—
476C4C11×#41614yes—
477C4C11×#52012yes—
478C4C11×#53511yescharacteristic
479C4C11×#53611yescharacteristic
480C2—24no—
481C2—82no—
482C2C11×#231111yescharacteristic
483C2C2×C11×#41611yescharacteristic
484C2C2×C11×#41711yescharacteristic
485C2C11×#324712yes—
486C2C11×#324812yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×C4⋊C8C2semidirect
3. C11×#2285C2semidirect
4. C11×#1989C2semidirect
5. C11×#1983C2semidirect
7. C11×#1892C2semidirect
8. C11×#1803C2semidirect
9. C11×#1802C2semidirect
12. C11×#529C4semidirect
94. #21887C11direct (N × H)
160. C22×C4⋊C8C2×C11semidirect
161. #2285C2×C11semidirect
162. #1989C2×C11semidirect
163. #1983C2×C11semidirect
165. #1892C2×C11semidirect
166. #1803C2×C11semidirect
167. #1802C2×C11semidirect
221. #529C4×C11semidirect
401. C11#21887direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5292
C22×C11×C4⋊C82
C11×#22852
C11×#19892
C11×#19832
C11×#18932
C11×#18922
C11×#18032
C11×#18022
#2188711