Finite Group Databasebeta

← C11×#21908 #14599101

Subgroups — C11×#21908 #14599101

Order 2816.

950 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2280C211yesmaximal, characteristic
2C11×#1924C214yesmaximal, complemented
3C11×#1923C214yesmaximal, complemented
4C11×#1798C212yesmaximal, complemented
5C11×#1779C212yesmaximal
6C11×#1750C212yesmaximal, complemented
7C24×C4×C11C2211yescharacteristic
8C2×C11×#117C2211yescharacteristic
9C2×C11×#117C2211yescharacteristic
10C2×C11×C4⋊C8C2212yescomplemented
11C2×C11×C4⋊C8C2212yescomplemented
12C2×C11×C22⋊C8C2214yes—
13C2×C11×C22⋊C8C2212yes—
14C2×C11×C22⋊C8C2214yes—
15C2×C11×C22⋊C8C2212yes—
16C2×C11×#97C2212yescomplemented
17C2×C4×C8×C11C2212yescomplemented
18C11×#381C412yes—
19C11×#380C412yes—
20C11×#380C412yes—
21C11×#379C412yes—
22C4×C11×C22⋊C4C2214yes—
23C11×#336C2214yescomplemented
24C11×#336C2214yescomplemented
25C25×C11C2×C411yescharacteristic
26C23×C4×C11—24no—
27C23×C4×C11—42no—
28C23×C4×C11—41no—
29C23×C4×C11—41no—
30C23×C4×C11C2×C412yes—
31C23×C4×C11C2×C411yescharacteristic
32C23×C4×C11C2312yes—
33C23×C4×C11C2311yescharacteristic
34C22×C8×C11C2314yes—
35C22×C8×C11C2314yes—
36C11×#117—41no—
37C11×#117—41no—
38C11×#117—42no—
39C2×C11×C4⋊C4C2×C412yes—
40C2×C11×C4⋊C4C2×C411yescharacteristic
41C2×C11×C4⋊C4C2×C411yescharacteristic
42C2×C11×C22⋊C4C2×C414yes—
43C2×C11×C22⋊C4C2×C412yes—
44C2×C11×C22⋊C4C2×C412yes—
45C2×C11×C22⋊C4C2×C414yes—
46C2×C42×C11C2312yes—
47C2×C42×C11C2312yes—
48C11×C4⋊C8—42no—
49C11×C4⋊C8—42no—
50C11×C22⋊C8—28no—
51C11×C22⋊C8—42no—
52C11×C22⋊C8—42no—
53C11×C22⋊C8—44no—
54C11×#97—42no—
55C4×C8×C11—42no—
56C11×#95C2×C414yes—
57C11×#95C2×C414yes—
58#21908C1111yesmaximal, characteristic, direct product factor, Sylow
59C24×C11—22no—
60C24×C11—24no—
61C24×C11—41no—
62C24×C11—41no—
63C24×C11—42no—
64C24×C11C22×C411yescharacteristic
65C24×C11C22×C412yes—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—24no—
71C22×C4×C11—24no—
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—24no—
75C22×C4×C11—42no—
76C22×C4×C11—42no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11—48no—
80C22×C4×C11—48no—
81C22×C4×C11C22×C412yes—
82C22×C4×C11C22×C412yes—
83C22×C4×C11C22×C414yes—
84C22×C4×C11C22×C412yes—
85C22×C4×C11C22×C411yescharacteristic
86C22×C4×C11#4114yes—
87C22×C4×C11C2411yescharacteristic
88C2×C8×C11—24no—
89C2×C8×C11—24no—
90C2×C8×C11—24no—
91C2×C8×C11—24no—
92C2×C8×C11—24no—
93C2×C8×C11—24no—
94C11×C4⋊C4—42no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C22⋊C4—28no—
98C11×C22⋊C4—44no—
99C11×C22⋊C4—42no—
100C11×C22⋊C4—42no—
101C42×C11—22no—
102C42×C11—22no—
103C42×C11—22no—
104C42×C11—22no—
105#2280C2×C1111yescharacteristic
106#1924C2×C1114yescomplemented
107#1923C2×C1114yescomplemented
108#1798C2×C1112yescomplemented
109#1779C2×C1112yes—
110#1750C2×C1112yescomplemented
111C23×C11—22no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—22no—
115C23×C11—22no—
116C23×C11—22no—
117C23×C11—22no—
118C23×C11—22no—
119C23×C11—22no—
120C23×C11—22no—
121C23×C11—48no—
122C23×C11—44no—
123C23×C11—44no—
124C23×C11—48no—
125C23×C11—44no—
126C23×C11#11712yes—
127C23×C11#13114yes—
128C23×C11C23×C411yescharacteristic
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—24no—
132C2×C4×C11—24no—
133C2×C4×C11—22no—
134C2×C4×C11—24no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—24no—
140C2×C4×C11—24no—
141C2×C4×C11—24no—
142C2×C4×C11—24no—
143C2×C4×C11—48no—
144C2×C4×C11—44no—
145C2×C4×C11—44no—
146C2×C4×C11—44no—
147C2×C4×C11#11712yes—
148C2×C4×C11C2×#4112yes—
149C2×C4×C11H(5,𝔽2)11yescharacteristic
150C2×C4×C11H(5,𝔽2)11yescharacteristic
151C2×C4×C11H(5,𝔽2)12yes—
152C8×C11—44no—
153C8×C11—44no—
154C24×C4C22×C1111yescharacteristic
155C2×#117C22×C1111yescharacteristic
156C2×#117C22×C1111yescharacteristic
157C2×C4⋊C8C22×C1112yescomplemented
158C2×C4⋊C8C22×C1112yescomplemented
159C2×C22⋊C8C22×C1114yes—
160C2×C22⋊C8C22×C1112yes—
161C2×C22⋊C8C22×C1114yes—
162C2×C22⋊C8C22×C1112yes—
163C2×#97C22×C1112yescomplemented
164C2×C4×C8C22×C1112yescomplemented
165#381C4×C1112yes—
166#380C4×C1112yes—
167#380C4×C1112yes—
168#379C4×C1112yes—
169C4×C22⋊C4C22×C1114yes—
170#336C22×C1114yescomplemented
171#336C22×C1114yescomplemented
172C22×C11—22no—
173C22×C11—24no—
174C22×C11—24no—
175C22×C11—24no—
176C22×C11—24no—
177C22×C11—416no—
178C22×C11—42no—
179C22×C11—42no—
180C22×C11—42no—
181C22×C11—42no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—42no—
185C22×C11C2×#11711yescharacteristic
186C22×C11#51811yescharacteristic
187C22×C11#51811yescharacteristic
188C22×C11C2×#13112yes—
189C22×C11#56812yes—
190C4×C11—22no—
191C4×C11—42no—
192C4×C11—44no—
193C4×C11—42no—
194C4×C11—42no—
195C4×C11#53812yes—
196C4×C11#53812yes—
197C25C2×C4×C1111yescharacteristic
198C23×C4—24no—
199C23×C4—42no—
200C23×C4—41no—
201C23×C4—41no—
202C23×C4C2×C4×C1112yes—
203C23×C4C2×C4×C1111yescharacteristic
204C23×C4C23×C1112yes—
205C23×C4C23×C1111yescharacteristic
206C22×C8C23×C1114yes—
207C22×C8C23×C1114yes—
208#117—41no—
209#117—41no—
210#117—42no—
211C2×C4⋊C4C2×C4×C1111yescharacteristic
212C2×C4⋊C4C2×C4×C1111yescharacteristic
213C2×C4⋊C4C2×C4×C1112yes—
214C2×C22⋊C4C2×C4×C1114yes—
215C2×C22⋊C4C2×C4×C1112yes—
216C2×C22⋊C4C2×C4×C1112yes—
217C2×C22⋊C4C2×C4×C1114yes—
218C2×C42C23×C1112yes—
219C2×C42C23×C1112yes—
220C4⋊C8—42no—
221C4⋊C8—42no—
222C22⋊C8—28no—
223C22⋊C8—42no—
224C22⋊C8—42no—
225C22⋊C8—44no—
226#97—42no—
227C4×C8—42no—
228#95C2×C4×C1114yes—
229#95C2×C4×C1114yes—
230C2×C11—42no—
231C2×C11—44no—
232C2×C11#231211yescharacteristic
233C2×C11#292412yes—
234C2×C11#297612yes—
235C2×C11#297711yescharacteristic
236C2×C11#297811yescharacteristic
237C24—22no—
238C24—24no—
239C24—41no—
240C24—41no—
241C24—42no—
242C24C22×C4×C1111yescharacteristic
243C24C22×C4×C1112yes—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—24no—
249C22×C4—24no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—24no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—48no—
258C22×C4—48no—
259C22×C4C22×C4×C1112yes—
260C22×C4C22×C4×C1112yes—
261C22×C4C22×C4×C1114yes—
262C22×C4C22×C4×C1112yes—
263C22×C4C22×C4×C1111yescharacteristic
264C22×C4C11×#4114yes—
265C22×C4C24×C1111yescharacteristic
266C2×C8—24no—
267C2×C8—24no—
268C2×C8—24no—
269C2×C8—24no—
270C2×C8—24no—
271C2×C8—24no—
272C4⋊C4—42no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C22⋊C4—28no—
276C22⋊C4—42no—
277C22⋊C4—42no—
278C22⋊C4—44no—
279C42—22no—
280C42—22no—
281C42—22no—
282C42—22no—
283C11#2190811yescharacteristic, direct product factor, Sylow
284C23—22no—
285C23—21no—
286C23—21no—
287C23—22no—
288C23—22no—
289C23—22no—
290C23—22no—
291C23—22no—
292C23—22no—
293C23—22no—
294C23—48no—
295C23—44no—
296C23—44no—
297C23—48no—
298C23—44no—
299C23C11×#11712yes—
300C23C11×#13114yes—
301C23C23×C4×C1111yescharacteristic
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—24no—
305C2×C4—24no—
306C2×C4—22no—
307C2×C4—24no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—48no—
317C2×C4—44no—
318C2×C4—44no—
319C2×C4—44no—
320C2×C4C11×#11712yes—
321C2×C4C2×C11×#4112yes—
322C2×C4C11×H(5,𝔽2)11yescharacteristic
323C2×C4C11×H(5,𝔽2)11yescharacteristic
324C2×C4C11×H(5,𝔽2)12yes—
325C8—44no—
326C8—44no—
327C22—24no—
328C22—24no—
329C22—24no—
330C22—24no—
331C22—22no—
332C22—416no—
333C22—42no—
334C22—42no—
335C22—42no—
336C22—41no—
337C22—41no—
338C22—42no—
339C22—42no—
340C22C2×C11×#11711yescharacteristic
341C22C11×#51811yescharacteristic
342C22C11×#51811yescharacteristic
343C22C2×C11×#13112yes—
344C22C11×#56812yes—
345C4—22no—
346C4—44no—
347C4—42no—
348C4—42no—
349C4—42no—
350C4C11×#53812yes—
351C4C11×#53812yes—
352C2—42no—
353C2—44no—
354C2C11×#231211yescharacteristic
355C2C11×#292412yes—
356C2C11×#297612yes—
357C2C11×#297711yescharacteristic
358C2C11×#297811yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC25×C11C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1924C2semidirect
3. C11×#1923C2semidirect
4. C11×#1798C2semidirect
6. C11×#1750C2semidirect
10. C2×C11×C4⋊C8C22semidirect
11. C2×C11×C4⋊C8C22semidirect
16. C2×C11×#97C22semidirect
17. C2×C4×C8×C11C22semidirect
23. C11×#336C22semidirect
24. C11×#336C22semidirect
58. #21908C11direct (N × H)
106. #1924C2×C11semidirect
107. #1923C2×C11semidirect
108. #1798C2×C11semidirect
110. #1750C2×C11semidirect
157. C2×C4⋊C8C22×C11semidirect
158. C2×C4⋊C8C22×C11semidirect
163. C2×#97C22×C11semidirect
164. C2×C4×C8C22×C11semidirect
170. #336C22×C11semidirect
171. #336C22×C11semidirect
283. C11#21908direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#22802
C11×#19242
C11×#19232
C11×#17982
C11×#17792
C11×#17502
#2190811