Finite Group Databasebeta

← C11×#21910 #14599103

Subgroups — C11×#21910 #14599103

Order 2816.

950 conjugacy classes of subgroups.

The subgroup lattice has 342 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⋊C8C2214yescomplemented
11C2×C11×C22⋊C8C2214yes—
12C2×C11×C22⋊C8C2212yes—
13C2×C11×C22⋊C8C2214yes—
14C2×C11×C22⋊C8C2212yes—
15C2×C11×#97C2212yescomplemented
16C2×C4×C8×C11C2212yescomplemented
17C11×#381C412yes—
18C11×#380C412yes—
19C11×#380C412yes—
20C11×#379C412yes—
21C4×C11×C22⋊C4C2214yes—
22C11×#336C2212yescomplemented
23C11×#336C2214yescomplemented
24C11×#336C2212yescomplemented
25C25×C11C2×C411yescharacteristic
26C23×C4×C11—24no—
27C23×C4×C11—42no—
28C23×C4×C11—42no—
29C23×C4×C11C2×C412yes—
30C23×C4×C11C2×C411yescharacteristic
31C23×C4×C11C2312yes—
32C23×C4×C11C2311yescharacteristic
33C22×C8×C11C2314yes—
34C22×C8×C11C2314yes—
35C11×#117—42no—
36C11×#117—42no—
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C11×C4⋊C4C2×C411yescharacteristic
39C2×C11×C4⋊C4C2×C412yes—
40C2×C11×C22⋊C4C2×C414yes—
41C2×C11×C22⋊C4C2×C412yes—
42C2×C11×C22⋊C4C2×C412yes—
43C2×C11×C22⋊C4C2×C414yes—
44C2×C42×C11C2312yes—
45C2×C42×C11C2312yes—
46C11×C4⋊C8—44no—
47C11×C22⋊C8—28no—
48C11×C22⋊C8—44no—
49C11×C22⋊C8—42no—
50C11×C22⋊C8—42no—
51C11×#97—42no—
52C4×C8×C11—42no—
53C11×#95C2×C414yes—
54C11×#95C2×C414yes—
55#21910C1111yesmaximal, characteristic, direct product factor, Sylow
56C24×C11—22no—
57C24×C11—24no—
58C24×C11—41no—
59C24×C11—41no—
60C24×C11—42no—
61C24×C11C22×C411yescharacteristic
62C24×C11C22×C412yes—
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—24no—
67C22×C4×C11—24no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—24no—
71C22×C4×C11—42no—
72C22×C4×C11—42no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11—416no—
76C22×C4×C11C22×C412yes—
77C22×C4×C11C22×C412yes—
78C22×C4×C11C22×C414yes—
79C22×C4×C11C22×C412yes—
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11#4114yes—
82C22×C4×C11C2411yescharacteristic
83C2×C8×C11—24no—
84C2×C8×C11—24no—
85C2×C8×C11—24no—
86C2×C8×C11—24no—
87C2×C8×C11—24no—
88C2×C8×C11—24no—
89C11×C4⋊C4—42no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C22⋊C4—28no—
93C11×C22⋊C4—44no—
94C11×C22⋊C4—42no—
95C11×C22⋊C4—42no—
96C42×C11—22no—
97C42×C11—22no—
98C42×C11—24no—
99#2280C2×C1111yescharacteristic
100#1924C2×C1114yescomplemented
101#1923C2×C1114yescomplemented
102#1798C2×C1112yescomplemented
103#1779C2×C1112yes—
104#1750C2×C1112yescomplemented
105C23×C11—22no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—22no—
109C23×C11—22no—
110C23×C11—22no—
111C23×C11—22no—
112C23×C11—22no—
113C23×C11—22no—
114C23×C11—22no—
115C23×C11—48no—
116C23×C11—44no—
117C23×C11—44no—
118C23×C11—48no—
119C23×C11—44no—
120C23×C11#11712yes—
121C23×C11#13114yes—
122C23×C11C23×C411yescharacteristic
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—28no—
126C2×C4×C11—22no—
127C2×C4×C11—24no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—24no—
133C2×C4×C11—24no—
134C2×C4×C11—24no—
135C2×C4×C11—24no—
136C2×C4×C11—48no—
137C2×C4×C11—44no—
138C2×C4×C11—44no—
139C2×C4×C11—44no—
140C2×C4×C11#11712yes—
141C2×C4×C11C2×#4112yes—
142C2×C4×C11H(5,𝔽2)12yes—
143C2×C4×C11H(5,𝔽2)12yes—
144C8×C11—44no—
145C8×C11—44no—
146C24×C4C22×C1111yescharacteristic
147C2×#117C22×C1111yescharacteristic
148C2×#117C22×C1111yescharacteristic
149C2×C4⋊C8C22×C1114yescomplemented
150C2×C22⋊C8C22×C1114yes—
151C2×C22⋊C8C22×C1112yes—
152C2×C22⋊C8C22×C1114yes—
153C2×C22⋊C8C22×C1112yes—
154C2×#97C22×C1112yescomplemented
155C2×C4×C8C22×C1112yescomplemented
156#381C4×C1112yes—
157#380C4×C1112yes—
158#380C4×C1112yes—
159#379C4×C1112yes—
160C4×C22⋊C4C22×C1114yes—
161#336C22×C1112yescomplemented
162#336C22×C1112yescomplemented
163#336C22×C1114yescomplemented
164C22×C11—22no—
165C22×C11—24no—
166C22×C11—24no—
167C22×C11—24no—
168C22×C11—24no—
169C22×C11—416no—
170C22×C11—42no—
171C22×C11—42no—
172C22×C11—42no—
173C22×C11—42no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—42no—
177C22×C11C2×#11711yescharacteristic
178C22×C11#51811yescharacteristic
179C22×C11#51811yescharacteristic
180C22×C11C2×#13112yes—
181C22×C11#56812yes—
182C4×C11—22no—
183C4×C11—42no—
184C4×C11—44no—
185C4×C11—42no—
186C4×C11—42no—
187C4×C11#53814yes—
188C25C2×C4×C1111yescharacteristic
189C23×C4—24no—
190C23×C4—42no—
191C23×C4—42no—
192C23×C4C2×C4×C1112yes—
193C23×C4C2×C4×C1111yescharacteristic
194C23×C4C23×C1112yes—
195C23×C4C23×C1111yescharacteristic
196C22×C8C23×C1114yes—
197C22×C8C23×C1114yes—
198#117—42no—
199#117—42no—
200C2×C4⋊C4C2×C4×C1112yes—
201C2×C4⋊C4C2×C4×C1111yescharacteristic
202C2×C4⋊C4C2×C4×C1111yescharacteristic
203C2×C22⋊C4C2×C4×C1114yes—
204C2×C22⋊C4C2×C4×C1112yes—
205C2×C22⋊C4C2×C4×C1112yes—
206C2×C22⋊C4C2×C4×C1114yes—
207C2×C42C23×C1112yes—
208C2×C42C23×C1112yes—
209C4⋊C8—44no—
210C22⋊C8—28no—
211C22⋊C8—44no—
212C22⋊C8—42no—
213C22⋊C8—42no—
214#97—42no—
215C4×C8—42no—
216#95C2×C4×C1114yes—
217#95C2×C4×C1114yes—
218C2×C11—42no—
219C2×C11—44no—
220C2×C11#231211yescharacteristic
221C2×C11#292412yes—
222C2×C11#297612yes—
223C2×C11#297711yescharacteristic
224C2×C11#297811yescharacteristic
225C24—22no—
226C24—24no—
227C24—41no—
228C24—41no—
229C24—42no—
230C24C22×C4×C1111yescharacteristic
231C24C22×C4×C1112yes—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—24no—
236C22×C4—24no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—24no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—416no—
245C22×C4C22×C4×C1112yes—
246C22×C4C22×C4×C1112yes—
247C22×C4C22×C4×C1114yes—
248C22×C4C22×C4×C1112yes—
249C22×C4C22×C4×C1111yescharacteristic
250C22×C4C11×#4114yes—
251C22×C4C24×C1111yescharacteristic
252C2×C8—24no—
253C2×C8—24no—
254C2×C8—24no—
255C2×C8—24no—
256C2×C8—24no—
257C2×C8—24no—
258C4⋊C4—42no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C22⋊C4—28no—
262C22⋊C4—42no—
263C22⋊C4—42no—
264C22⋊C4—44no—
265C42—22no—
266C42—22no—
267C42—24no—
268C11#2191011yescharacteristic, direct product factor, Sylow
269C23—22no—
270C23—21no—
271C23—21no—
272C23—22no—
273C23—22no—
274C23—22no—
275C23—22no—
276C23—22no—
277C23—22no—
278C23—22no—
279C23—48no—
280C23—44no—
281C23—44no—
282C23—48no—
283C23—44no—
284C23C11×#11712yes—
285C23C11×#13114yes—
286C23C23×C4×C1111yescharacteristic
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—28no—
290C2×C4—22no—
291C2×C4—24no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—24no—
299C2×C4—24no—
300C2×C4—48no—
301C2×C4—44no—
302C2×C4—44no—
303C2×C4—44no—
304C2×C4C11×#11712yes—
305C2×C4C2×C11×#4112yes—
306C2×C4C11×H(5,𝔽2)12yes—
307C2×C4C11×H(5,𝔽2)12yes—
308C8—44no—
309C8—44no—
310C22—24no—
311C22—24no—
312C22—24no—
313C22—24no—
314C22—22no—
315C22—416no—
316C22—42no—
317C22—42no—
318C22—42no—
319C22—41no—
320C22—41no—
321C22—42no—
322C22—42no—
323C22C2×C11×#11711yescharacteristic
324C22C11×#51811yescharacteristic
325C22C11×#51811yescharacteristic
326C22C2×C11×#13112yes—
327C22C11×#56812yes—
328C4—22no—
329C4—44no—
330C4—42no—
331C4—42no—
332C4—42no—
333C4C11×#53814yes—
334C2—42no—
335C2—44no—
336C2C11×#231211yescharacteristic
337C2C11×#292412yes—
338C2C11×#297612yes—
339C2C11×#297711yescharacteristic
340C2C11×#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
15. C2×C11×#97C22semidirect
16. C2×C4×C8×C11C22semidirect
22. C11×#336C22semidirect
23. C11×#336C22semidirect
24. C11×#336C22semidirect
55. #21910C11direct (N × H)
100. #1924C2×C11semidirect
101. #1923C2×C11semidirect
102. #1798C2×C11semidirect
104. #1750C2×C11semidirect
149. C2×C4⋊C8C22×C11semidirect
154. C2×#97C22×C11semidirect
155. C2×C4×C8C22×C11semidirect
161. #336C22×C11semidirect
162. #336C22×C11semidirect
163. #336C22×C11semidirect
268. C11#21910direct (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
#2191011