Finite Group Databasebeta

← C11×#21886 #14599079

Subgroups — C11×#21886 #14599079

Order 2816.

1150 conjugacy classes of subgroups.

The subgroup lattice has 460 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×#2283C211yesmaximal, characteristic, complemented
4C11×#1989C212yesmaximal, complemented
5C11×#1983C212yesmaximal, complemented
6C11×#1893C212yesmaximal
7C11×#1892C212yesmaximal, complemented
8C11×#1805C212yesmaximal, complemented
9C11×#1804C212yesmaximal, 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—
23C22×C42×C11C2211yescharacteristic
24C2×C11×C4⋊C8—24no—
25C2×C11×C4⋊C8C2212yes—
26C2×C11×C4⋊C8C2212yes—
27C2×C11×#103C2214yes—
28C2×C11×#102C2214yes—
29C11×#383—21no—
30C11×#382C2212yes—
31C11×#381—21no—
32C11×#380C2212yes—
33C4×C11×C4⋊C4C2212yes—
34C4×C11×C22⋊C4—21no—
35C11×#376—21no—
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—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2314yes—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—22no—
77C2×C42×C11—21no—
78C2×C42×C11—22no—
79C2×C42×C11C2×C414yes—
80C2×C42×C11D411yescharacteristic
81C2×C42×C11D411yescharacteristic
82C2×C42×C11D414yes—
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C11×C4⋊C8—24no—
86C11×C4⋊C8—24no—
87C11×#103—44no—
88C11×#102—44no—
89C11×#95—22no—
90C11×#95—22no—
91C11×#95—22no—
92C11×#95—22no—
93#21886C1111yesmaximal, characteristic, direct product factor, Sylow
94C24×C11—21no—
95C24×C11C2×D411yescharacteristic
96C2×Q8×C11—21no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11C22×C412yes—
100C2×D4×C11—24no—
101C2×D4×C11—21no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—44no—
105C2×D4×C11C22×C412yes—
106C22×C4×C11—24no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—24no—
113C22×C4×C11—24no—
114C22×C4×C11—42no—
115C22×C4×C11—44no—
116C22×C4×C11C22⋊C414yes—
117C22×C4×C11C22⋊C414yes—
118C22×C4×C11C22×C412yes—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2411yescharacteristic
126C2×C8×C11—24no—
127C2×C8×C11—24no—
128C2×C8×C11—24no—
129C2×C8×C11—48no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—24no—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—24no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—24no—
138C11×C4⋊C4C22×C412yes—
139C11×C4⋊C4C22×C412yes—
140C11×C22⋊C4—24no—
141C11×C22⋊C4—24no—
142C11×C22⋊C4—24no—
143C11×C22⋊C4—24no—
144C11×C22⋊C4—24no—
145C11×C22⋊C4—44no—
146C42×C11—24no—
147C42×C11—44no—
148C42×C11C22⋊C414yes—
149C42×C11C22⋊C414yes—
150C42×C11C22×C412yes—
151C42×C11C22×C412yes—
152C42×C11C2×D412yes—
153C42×C11C2×D412yes—
154C2×#529C2×C1111yescharacteristic
155C22×C4⋊C8C2×C1111yescharacteristic, complemented
156#2283C2×C1111yescharacteristic, complemented
157#1989C2×C1112yescomplemented
158#1983C2×C1112yescomplemented
159#1893C2×C1112yes—
160#1892C2×C1112yescomplemented
161#1805C2×C1112yescomplemented
162#1804C2×C1112yescomplemented
163C23×C11—22no—
164C23×C11—22no—
165C23×C11—22no—
166C23×C11—42no—
167C23×C11—42no—
168C23×C11—42no—
169C23×C11C2×C22⋊C412yes—
170C23×C11#13514yes—
171C23×C11C22×D411yescharacteristic
172Q8×C11—24no—
173Q8×C11—41no—
174Q8×C11—41no—
175D4×C11—24no—
176D4×C11—48no—
177D4×C11—41no—
178D4×C11—41no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—28no—
185C2×C4×C11—24no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—44no—
192C2×C4×C11—48no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—44no—
197C2×C4×C11—44no—
198C2×C4×C11—44no—
199C2×C4×C11C2×C22⋊C412yes—
200C2×C4×C11C2×C22⋊C412yes—
201C2×C4×C11C2×C22⋊C412yes—
202C2×C4×C11C2×C22⋊C412yes—
203C2×C4×C11C2×C22⋊C412yes—
204C2×C4×C11C23×C411yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11H(5,𝔽2)12yes—
207C2×C4×C112−1+412yes—
208C8×C11—44no—
209C23×C8C22×C1112yes—
210#529—24no—
211#529C4×C1118yescomplemented
212C2×#126—21no—
213C2×#125C22×C1111yescharacteristic
214C2×#124C22×C1111yescharacteristic
215C2×#123—21no—
216C2×C22⋊Q8C22×C1111yescharacteristic
217C2×#121C22×C1111yescharacteristic
218C2×C4×Q8C22×C1111yescharacteristic
219C2×C4×D4—21no—
220C2×C4×D4C22×C1111yescharacteristic
221C2×#117—21no—
222C22×C42C22×C1111yescharacteristic
223C2×C4⋊C8—24no—
224C2×C4⋊C8C22×C1112yes—
225C2×C4⋊C8C22×C1112yes—
226C2×#103C22×C1114yes—
227C2×#102C22×C1114yes—
228#383—21no—
229#382C22×C1112yes—
230#381—21no—
231#380C22×C1112yes—
232C4×C4⋊C4C22×C1112yes—
233C4×C22⋊C4—21no—
234#376—21no—
235#340C22×C1114yes—
236#340C22×C1114yes—
237C22×C11—22no—
238C22×C11—22no—
239C22×C11—28no—
240C22×C11—42no—
241C22×C11—42no—
242C22×C11—42no—
243C22×C11—84no—
244C22×C11#41614yes—
245C22×C11C22×C22⋊C411yescharacteristic
246C22×C11#53712yes—
247C22×C11C2×#13512yes—
248C22×C11#57512yes—
249C4×C11—22no—
250C4×C11—22no—
251C4×C11—22no—
252C4×C11—22no—
253C4×C11—22no—
254C4×C11—42no—
255C4×C11—42no—
256C4×C11—42no—
257C4×C11—84no—
258C4×C11#52012yes—
259C4×C11#53511yescharacteristic
260C4×C11#53611yescharacteristic
261C22×Q8C23×C1111yescharacteristic
262C22×D4—21no—
263C22×D4C23×C1111yescharacteristic
264C23×C4—21no—
265C23×C4D4×C1111yescharacteristic
266C23×C4D4×C1111yescharacteristic
267C23×C4C23×C1111yescharacteristic
268C22×C8—24no—
269C22×C8—44no—
270C22×C8C23×C1114yes—
271#126—28no—
272#125—22no—
273#125C2×C4×C1114yes—
274#124—22no—
275#124C2×C4×C1114yes—
276#123—28no—
277C22⋊Q8—22no—
278C22⋊Q8C2×C4×C1114yes—
279#121—22no—
280#121C2×C4×C1114yes—
281C4×Q8—22no—
282C4×Q8C2×C4×C1114yes—
283C4×D4—28no—
284C4×D4—22no—
285C4×D4C2×C4×C1114yes—
286#117—28no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4C23×C1114yes—
292C2×C4⋊C4C23×C1111yescharacteristic
293C2×C4⋊C4C23×C1111yescharacteristic
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—21no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—22no—
300C2×C42—21no—
301C2×C42—22no—
302C2×C42C2×C4×C1114yes—
303C2×C42D4×C1111yescharacteristic
304C2×C42D4×C1111yescharacteristic
305C2×C42D4×C1114yes—
306C2×C42C23×C1111yescharacteristic
307C2×C42C23×C1111yescharacteristic
308C4⋊C8—24no—
309C4⋊C8—24no—
310#103—44no—
311#102—44no—
312#95—22no—
313#95—22no—
314#95—22no—
315#95—22no—
316C2×C11—24no—
317C2×C11—82no—
318C2×C11#231111yescharacteristic
319C2×C11C2×#41611yescharacteristic
320C2×C11#289611yescharacteristic
321C2×C11#325014yes—
322C24—21no—
323C24C2×D4×C1111yescharacteristic
324C2×Q8—21no—
325C2×Q8—22no—
326C2×Q8—22no—
327C2×Q8C22×C4×C1112yes—
328C2×D4—24no—
329C2×D4—21no—
330C2×D4—22no—
331C2×D4—22no—
332C2×D4—44no—
333C2×D4C22×C4×C1112yes—
334C22×C4—24no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—24no—
341C22×C4—24no—
342C22×C4—42no—
343C22×C4—44no—
344C22×C4C11×C22⋊C414yes—
345C22×C4C11×C22⋊C414yes—
346C22×C4C22×C4×C1112yes—
347C22×C4C2×D4×C1111yescharacteristic
348C22×C4C2×D4×C1111yescharacteristic
349C22×C4C2×D4×C1111yescharacteristic
350C22×C4C2×D4×C1111yescharacteristic
351C22×C4C2×D4×C1111yescharacteristic
352C22×C4C2×D4×C1112yes—
353C22×C4C24×C1111yescharacteristic
354C2×C8—24no—
355C2×C8—24no—
356C2×C8—24no—
357C2×C8—48no—
358C4⋊C4—24no—
359C4⋊C4—24no—
360C4⋊C4—24no—
361C4⋊C4—24no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—24no—
365C4⋊C4—24no—
366C4⋊C4C22×C4×C1112yes—
367C4⋊C4C22×C4×C1112yes—
368C22⋊C4—24no—
369C22⋊C4—24no—
370C22⋊C4—24no—
371C22⋊C4—24no—
372C22⋊C4—24no—
373C22⋊C4—44no—
374C42—24no—
375C42—44no—
376C42C11×C22⋊C414yes—
377C42C11×C22⋊C414yes—
378C42C22×C4×C1112yes—
379C42C22×C4×C1112yes—
380C42C2×D4×C1112yes—
381C42C2×D4×C1112yes—
382C11#2188611yescharacteristic, direct product factor, Sylow
383C23—22no—
384C23—22no—
385C23—22no—
386C23—42no—
387C23—42no—
388C23—42no—
389C23C2×C11×C22⋊C412yes—
390C23C11×#13514yes—
391C23C22×D4×C1111yescharacteristic
392Q8—24no—
393Q8—41no—
394Q8—41no—
395D4—24no—
396D4—48no—
397D4—41no—
398D4—41no—
399C2×C4—22no—
400C2×C4—28no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—24no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—44no—
412C2×C4—48no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—44no—
417C2×C4—44no—
418C2×C4—44no—
419C2×C4C2×C11×C22⋊C412yes—
420C2×C4C2×C11×C22⋊C412yes—
421C2×C4C2×C11×C22⋊C412yes—
422C2×C4C2×C11×C22⋊C412yes—
423C2×C4C2×C11×C22⋊C412yes—
424C2×C4C23×C4×C1111yescharacteristic
425C2×C4C22×D4×C1111yescharacteristic
426C2×C4C11×H(5,𝔽2)12yes—
427C2×C4C11×2−1+412yes—
428C8—44no—
429C22—22no—
430C22—28no—
431C22—22no—
432C22—42no—
433C22—42no—
434C22—42no—
435C22—84no—
436C22C11×#41614yes—
437C22C22×C11×C22⋊C411yescharacteristic
438C22C11×#53712yes—
439C22C2×C11×#13512yes—
440C22C11×#57512yes—
441C4—22no—
442C4—22no—
443C4—22no—
444C4—22no—
445C4—22no—
446C4—42no—
447C4—42no—
448C4—42no—
449C4—84no—
450C4C11×#52012yes—
451C4C11×#53511yescharacteristic
452C4C11×#53611yescharacteristic
453C2—24no—
454C2—82no—
455C2C11×#231111yescharacteristic
456C2C2×C11×#41611yescharacteristic
457C2C11×#289611yescharacteristic
458C2C11×#325014yes—
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×#2283C2semidirect
4. C11×#1989C2semidirect
5. C11×#1983C2semidirect
7. C11×#1892C2semidirect
8. C11×#1805C2semidirect
9. C11×#1804C2semidirect
12. C11×#529C4semidirect
93. #21886C11direct (N × H)
155. C22×C4⋊C8C2×C11semidirect
156. #2283C2×C11semidirect
157. #1989C2×C11semidirect
158. #1983C2×C11semidirect
160. #1892C2×C11semidirect
161. #1805C2×C11semidirect
162. #1804C2×C11semidirect
211. #529C4×C11semidirect
382. C11#21886direct (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×#22832
C11×#19892
C11×#19832
C11×#18932
C11×#18922
C11×#18052
C11×#18042
#2188611