Finite Group Databasebeta

← C11×#21866 #14599059

Subgroups — C11×#21866 #14599059

Order 2816.

1114 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#533C211yesmaximal, characteristic
2C2×C11×#432C211yesmaximal, characteristic
3C2×C11×#382C211yesmaximal, characteristic
4C11×#1993C212yesmaximal, complemented
5C11×#1960C212yesmaximal, complemented
6C11×#1872C214yesmaximal
7C11×#1805C214yesmaximal, complemented
8C11×#533—24no—
9C11×#533C418yescomplemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C11×#125—21no—
13C2×C11×C22⋊Q8—21no—
14C2×C11×C22⋊Q8C2212yes—
15C2×C4×Q8×C11—21no—
16C2×C4×Q8×C11C2212yes—
17C2×C11×#117—21no—
18C22×C11×C4⋊C4C2212yes—
19C22×C42×C11C2211yescharacteristic
20C11×#432—24no—
21C2×C11×C4⋊C8C2212yes—
22C2×C11×#103C2218yes—
23C2×C11×C22⋊C8C2212yes—
24C2×C11×#97C2212yes—
25C11×#382—21no—
26C11×#382—21no—
27C11×#382C2212yes—
28C11×#382C2212yes—
29C2×C11×#95—21no—
30C2×C11×#95—21no—
31C11×#340C2218yes—
32C22×Q8×C11—21no—
33C22×Q8×C11C2312yes—
34C23×C4×C11—22no—
35C23×C4×C11D411yescharacteristic
36C23×C4×C11D411yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C22×C8×C11C2314yes—
39C11×C4⋊Q8—22no—
40C11×C4⋊Q8—22no—
41C11×C4⋊Q8C2×C414yescomplemented
42C11×C4⋊Q8C2×C414yescomplemented
43C11×#125—28no—
44C11×C22⋊Q8—28no—
45C11×C22⋊Q8—24no—
46C11×C22⋊Q8C2×C418yes—
47C4×Q8×C11—28no—
48C4×Q8×C11—24no—
49C4×Q8×C11C2×C418yescomplemented
50C11×#117—28no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—44no—
58C2×C11×C4⋊C4C2314yes—
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C22⋊C4—22no—
61C2×C42×C11—22no—
62C2×C42×C11C2×C414yes—
63C2×C42×C11D411yescharacteristic
64C2×C42×C11D411yescharacteristic
65C2×C42×C11D414yes—
66C2×C42×C11C2311yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C11×C4⋊C8—24no—
69C11×#103—48no—
70C11×C22⋊C8—24no—
71C11×#97—24no—
72C11×#95—22no—
73C11×#95—22no—
74C11×#95—22no—
75C11×#95—22no—
76#21866C1111yesmaximal, characteristic, direct product factor, Sylow
77C24×C11C2×D411yescharacteristic
78C2×Q8×C11—24no—
79C2×Q8×C11—22no—
80C2×Q8×C11—24no—
81C2×Q8×C11—24no—
82C2×Q8×C11—44no—
83C2×Q8×C11C22×C414yes—
84C22×C4×C11—24no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—24no—
90C22×C4×C11—42no—
91C22×C4×C11—44no—
92C22×C4×C11—44no—
93C22×C4×C11—44no—
94C22×C4×C11C22⋊C414yes—
95C22×C4×C11C22⋊C414yes—
96C22×C4×C11C22×C412yes—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2411yescharacteristic
104C2×C8×C11—24no—
105C2×C8×C11—24no—
106C2×C8×C11—24no—
107C11×C4⋊C4—24no—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—24no—
110C11×C4⋊C4—28no—
111C11×C4⋊C4—28no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—28no—
114C11×C4⋊C4—44no—
115C11×C4⋊C4C22×C414yes—
116C11×C22⋊C4—28no—
117C42×C11—28no—
118C42×C11C22⋊C414yes—
119C42×C11C22⋊C414yes—
120C42×C11C22×C412yes—
121C42×C11C22×C412yes—
122C42×C11C2×D412yes—
123C42×C11C2×D412yes—
124C2×#533C2×C1111yescharacteristic
125C2×#432C2×C1111yescharacteristic
126C2×#382C2×C1111yescharacteristic
127#1993C2×C1112yescomplemented
128#1960C2×C1112yescomplemented
129#1872C2×C1114yes—
130#1805C2×C1114yescomplemented
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—22no—
134C23×C11C2×C22⋊C412yes—
135C23×C11#13714yes—
136C23×C11C22×D411yescharacteristic
137Q8×C11—28no—
138Q8×C11—48no—
139Q8×C11—44no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—28no—
147C2×C4×C11—24no—
148C2×C4×C11—24no—
149C2×C4×C11—24no—
150C2×C4×C11—24no—
151C2×C4×C11—44no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—44no—
155C2×C4×C11—44no—
156C2×C4×C11—44no—
157C2×C4×C11—44no—
158C2×C4×C11—88no—
159C2×C4×C11C2×C22⋊C412yes—
160C2×C4×C11C2×C22⋊C412yes—
161C2×C4×C11C2×C22⋊C412yes—
162C2×C4×C11C2×C22⋊C412yes—
163C2×C4×C11C2×C22⋊C412yes—
164C2×C4×C11C23×C411yescharacteristic
165C2×C4×C11C22×D411yescharacteristic
166C2×C4×C11H(5,𝔽2)12yes—
167C2×C4×C112−1+412yes—
168C8×C11—44no—
169#533—24no—
170#533C4×C1118yescomplemented
171C2×C4⋊Q8C22×C1111yescharacteristic
172C2×C4⋊Q8C22×C1111yescharacteristic
173C2×#125—21no—
174C2×C22⋊Q8—21no—
175C2×C22⋊Q8C22×C1112yes—
176C2×C4×Q8—21no—
177C2×C4×Q8C22×C1112yes—
178C2×#117—21no—
179C22×C4⋊C4C22×C1112yes—
180C22×C42C22×C1111yescharacteristic
181#432—24no—
182C2×C4⋊C8C22×C1112yes—
183C2×#103C22×C1118yes—
184C2×C22⋊C8C22×C1112yes—
185C2×#97C22×C1112yes—
186#382—21no—
187#382—21no—
188#382C22×C1112yes—
189#382C22×C1112yes—
190C2×#95—21no—
191C2×#95—21no—
192#340C22×C1118yes—
193C22×C11—22no—
194C22×C11—22no—
195C22×C11—24no—
196C22×C11—24no—
197C22×C11#41914yes—
198C22×C11C22×C22⋊C411yescharacteristic
199C22×C11#53511yescharacteristic
200C22×C11#53611yescharacteristic
201C22×C11C2×#13712yes—
202C22×C11#57512yes—
203C4×C11—22no—
204C4×C11—22no—
205C4×C11—22no—
206C4×C11—22no—
207C4×C11—22no—
208C4×C11—44no—
209C4×C11—44no—
210C4×C11—84no—
211C4×C11#52012yes—
212C4×C11#53712yes—
213C22×Q8—21no—
214C22×Q8C23×C1112yes—
215C23×C4—22no—
216C23×C4D4×C1111yescharacteristic
217C23×C4D4×C1111yescharacteristic
218C23×C4C23×C1111yescharacteristic
219C22×C8C23×C1114yes—
220C4⋊Q8—22no—
221C4⋊Q8—22no—
222C4⋊Q8C2×C4×C1114yescomplemented
223C4⋊Q8C2×C4×C1114yescomplemented
224#125—28no—
225C22⋊Q8—28no—
226C22⋊Q8—24no—
227C22⋊Q8C2×C4×C1118yes—
228C4×Q8—28no—
229C4×Q8—24no—
230C4×Q8C2×C4×C1118yescomplemented
231#117—28no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—44no—
239C2×C4⋊C4C23×C1114yes—
240C2×C4⋊C4C23×C1112yes—
241C2×C22⋊C4—22no—
242C2×C42—22no—
243C2×C42C2×C4×C1114yes—
244C2×C42D4×C1111yescharacteristic
245C2×C42D4×C1111yescharacteristic
246C2×C42D4×C1114yes—
247C2×C42C23×C1111yescharacteristic
248C2×C42C23×C1111yescharacteristic
249C4⋊C8—24no—
250#103—48no—
251C22⋊C8—24no—
252#97—24no—
253#95—22no—
254#95—22no—
255#95—22no—
256#95—22no—
257C2×C11—24no—
258C2×C11#231111yescharacteristic
259C2×C11C2×#41911yescharacteristic
260C2×C11#289611yescharacteristic
261C2×C11#321512yes—
262C2×C11#323612yes—
263C24C2×D4×C1111yescharacteristic
264C2×Q8—24no—
265C2×Q8—22no—
266C2×Q8—24no—
267C2×Q8—24no—
268C2×Q8—44no—
269C2×Q8C22×C4×C1114yes—
270C22×C4—24no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—24no—
276C22×C4—42no—
277C22×C4—44no—
278C22×C4—44no—
279C22×C4—44no—
280C22×C4C11×C22⋊C414yes—
281C22×C4C11×C22⋊C414yes—
282C22×C4C22×C4×C1112yes—
283C22×C4C2×D4×C1111yescharacteristic
284C22×C4C2×D4×C1111yescharacteristic
285C22×C4C2×D4×C1111yescharacteristic
286C22×C4C2×D4×C1111yescharacteristic
287C22×C4C2×D4×C1111yescharacteristic
288C22×C4C2×D4×C1112yes—
289C22×C4C24×C1111yescharacteristic
290C2×C8—24no—
291C2×C8—24no—
292C2×C8—24no—
293C4⋊C4—24no—
294C4⋊C4—24no—
295C4⋊C4—24no—
296C4⋊C4—28no—
297C4⋊C4—28no—
298C4⋊C4—22no—
299C4⋊C4—28no—
300C4⋊C4—44no—
301C4⋊C4C22×C4×C1114yes—
302C22⋊C4—28no—
303C42—28no—
304C42C11×C22⋊C414yes—
305C42C11×C22⋊C414yes—
306C42C22×C4×C1112yes—
307C42C22×C4×C1112yes—
308C42C2×D4×C1112yes—
309C42C2×D4×C1112yes—
310C11#2186611yescharacteristic, direct product factor, Sylow
311C23—21no—
312C23—21no—
313C23—22no—
314C23C2×C11×C22⋊C412yes—
315C23C11×#13714yes—
316C23C22×D4×C1111yescharacteristic
317Q8—28no—
318Q8—48no—
319Q8—44no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—28no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—24no—
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—24no—
331C2×C4—44no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—44no—
335C2×C4—44no—
336C2×C4—44no—
337C2×C4—44no—
338C2×C4—88no—
339C2×C4C2×C11×C22⋊C412yes—
340C2×C4C2×C11×C22⋊C412yes—
341C2×C4C2×C11×C22⋊C412yes—
342C2×C4C2×C11×C22⋊C412yes—
343C2×C4C2×C11×C22⋊C412yes—
344C2×C4C23×C4×C1111yescharacteristic
345C2×C4C22×D4×C1111yescharacteristic
346C2×C4C11×H(5,𝔽2)12yes—
347C2×C4C11×2−1+412yes—
348C8—44no—
349C22—22no—
350C22—24no—
351C22—24no—
352C22—22no—
353C22C11×#41914yes—
354C22C22×C11×C22⋊C411yescharacteristic
355C22C11×#53511yescharacteristic
356C22C11×#53611yescharacteristic
357C22C2×C11×#13712yes—
358C22C11×#57512yes—
359C4—22no—
360C4—22no—
361C4—22no—
362C4—22no—
363C4—22no—
364C4—44no—
365C4—44no—
366C4—84no—
367C4C11×#52012yes—
368C4C11×#53712yes—
369C2—24no—
370C2C11×#231111yescharacteristic
371C2C2×C11×#41911yescharacteristic
372C2C11×#289611yescharacteristic
373C2C11×#321512yes—
374C2C11×#323612yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
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
4. C11×#1993C2semidirect
5. C11×#1960C2semidirect
7. C11×#1805C2semidirect
9. C11×#533C4semidirect
41. C11×C4⋊Q8C2×C4semidirect
42. C11×C4⋊Q8C2×C4semidirect
49. C4×Q8×C11C2×C4semidirect
76. #21866C11direct (N × H)
127. #1993C2×C11semidirect
128. #1960C2×C11semidirect
130. #1805C2×C11semidirect
170. #533C4×C11semidirect
222. C4⋊Q8C2×C4×C11semidirect
223. C4⋊Q8C2×C4×C11semidirect
230. C4×Q8C2×C4×C11semidirect
310. C11#21866direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5332
C2×C11×#4322
C2×C11×#3822
C11×#19932
C11×#19602
C11×#18722
C11×#18052
#2186611