Finite Group Databasebeta

← C11×#21942 #14599135

Subgroups — C11×#21942 #14599135

Order 2816.

1234 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#407C211yesmaximal, characteristic
2C2×C11×#380C212yesmaximal
3C11×#1853C214yesmaximal, complemented
4C11×#1852C214yesmaximal, complemented
5C11×#1809C214yesmaximal, complemented
6C24×C4×C11C2211yescharacteristic
7C22×C11×M16C2212yes—
8C22×C11×C4⋊C4C2212yes—
9C22×C11×C4⋊C4C2212yes—
10C22×C11×C22⋊C4—22no—
11C2×C11×#107C2214yescomplemented
12C2×C11×#106C2214yescomplemented
13C11×#407C418yescomplemented
14C2×C11×C22⋊C8C2214yes—
15C11×#380—22no—
16C11×#380—22no—
17C11×#380C2214yes—
18C11×#380C2214yes—
19C2×C11×#95—22no—
20C11×#340C2218yescomplemented
21C25×C11D411yescharacteristic
22C23×C4×C11—22no—
23C23×C4×C11—22no—
24C23×C4×C11—42no—
25C23×C4×C11—42no—
26C23×C4×C11C2×C414yes—
27C23×C4×C11D412yes—
28C23×C4×C11D411yescharacteristic
29C23×C4×C11Q814yes—
30C23×C4×C11C2312yes—
31C23×C4×C11C2311yescharacteristic
32C2×C11×M16—42no—
33C2×C11×M16—42no—
34C2×C11×M16C2×C418yescomplemented
35C22×C8×C11C2314yes—
36C2×C11×C4⋊C4—22no—
37C2×C11×C4⋊C4—22no—
38C2×C11×C4⋊C4—44no—
39C2×C11×C4⋊C4—44no—
40C2×C11×C4⋊C4C2314yes—
41C2×C11×C4⋊C4C2314yes—
42C2×C11×C22⋊C4—24no—
43C2×C11×C22⋊C4—24no—
44C2×C11×C22⋊C4—48no—
45C11×#107—44no—
46C11×#106—44no—
47C11×C22⋊C8C2×C4116yescomplemented
48C11×#95—24no—
49C11×#95—24no—
50#21942C1111yesmaximal, characteristic, direct product factor, Sylow
51C24×C11—24no—
52C24×C11—24no—
53C24×C11—41no—
54C24×C11—41no—
55C24×C11C4⋊C414yes—
56C24×C11C2×D411yescharacteristic
57C24×C11C2×D412yes—
58C22×C4×C11—24no—
59C22×C4×C11—24no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—24no—
63C22×C4×C11—24no—
64C22×C4×C11—48no—
65C22×C4×C11—48no—
66C22×C4×C11—41no—
67C22×C4×C11—41no—
68C22×C4×C11—42no—
69C22×C4×C11—42no—
70C22×C4×C11—44no—
71C22×C4×C11—44no—
72C22×C4×C11—44no—
73C22×C4×C11—44no—
74C22×C4×C11—44no—
75C22×C4×C11—44no—
76C22×C4×C11C4⋊C414yes—
77C22×C4×C11C4⋊C418yes—
78C22×C4×C11C22×C414yes—
79C22×C4×C11C22×C412yes—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D412yes—
82C22×C4×C11C2×Q812yes—
83C22×C4×C11C2×Q814yes—
84C22×C4×C11C2411yescharacteristic
85C11×M16—48no—
86C2×C8×C11—24no—
87C2×C8×C11—24no—
88C2×C8×C11C22×C418yes—
89C11×C4⋊C4—28no—
90C11×C4⋊C4—28no—
91C11×C4⋊C4—44no—
92C11×C4⋊C4—44no—
93C11×C22⋊C4—48no—
94C11×C22⋊C4—48no—
95C2×#407C2×C1111yescharacteristic
96C2×#380C2×C1112yes—
97#1853C2×C1114yescomplemented
98#1852C2×C1114yescomplemented
99#1809C2×C1114yescomplemented
100C23×C11—22no—
101C23×C11—22no—
102C23×C11—22no—
103C23×C11—22no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—22no—
107C23×C11—22no—
108C23×C11—216no—
109C23×C11—44no—
110C23×C11—44no—
111C23×C11—48no—
112C23×C11—44no—
113C23×C11C2×C4⋊C412yes—
114C23×C11C2×C4⋊C414yes—
115C23×C11AGL(1,ℤ/8)14yes—
116C23×C11#13714yes—
117C23×C11C22×D411yescharacteristic
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—24no—
123C2×C4×C11—28no—
124C2×C4×C11—28no—
125C2×C4×C11—24no—
126C2×C4×C11—48no—
127C2×C4×C11—44no—
128C2×C4×C11—44no—
129C2×C4×C11—44no—
130C2×C4×C11—44no—
131C2×C4×C11—44no—
132C2×C4×C11—44no—
133C2×C4×C11—44no—
134C2×C4×C11—88no—
135C2×C4×C11—88no—
136C2×C4×C11C2×C4⋊C414yes—
137C2×C4×C11C2×C4⋊C412yes—
138C2×C4×C11C23×C411yescharacteristic
139C2×C4×C11C22×Q811yescharacteristic
140C2×C4×C11H(5,𝔽2)12yes—
141C2×C4×C11H(5,𝔽2)12yes—
142C8×C11—28no—
143C24×C4C22×C1111yescharacteristic
144C22×M16C22×C1112yes—
145C22×C4⋊C4C22×C1112yes—
146C22×C4⋊C4C22×C1112yes—
147C22×C22⋊C4—22no—
148C2×#107C22×C1114yescomplemented
149C2×#106C22×C1114yescomplemented
150#407C4×C1118yescomplemented
151C2×C22⋊C8C22×C1114yes—
152#380—22no—
153#380—22no—
154#380C22×C1114yes—
155#380C22×C1114yes—
156C2×#95—22no—
157#340C22×C1118yescomplemented
158C22×C11—24no—
159C22×C11—24no—
160C22×C11—24no—
161C22×C11—24no—
162C22×C11—24no—
163C22×C11—24no—
164C22×C11—22no—
165C22×C11—24no—
166C22×C11—416no—
167C22×C11—41no—
168C22×C11—42no—
169C22×C11—41no—
170C22×C11#42818yes—
171C22×C11C22×C4⋊C411yescharacteristic
172C22×C11#53411yescharacteristic
173C22×C11#53411yescharacteristic
174C22×C11C2×AGL(1,ℤ/8)12yes—
175C22×C11C2×#13712yes—
176C4×C11—24no—
177C4×C11—22no—
178C4×C11—84no—
179C4×C11—84no—
180C4×C11#51812yes—
181C4×C11#54312yes—
182C25D4×C1111yescharacteristic
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—42no—
186C23×C4—42no—
187C23×C4C2×C4×C1114yes—
188C23×C4D4×C1112yes—
189C23×C4D4×C1111yescharacteristic
190C23×C4Q8×C1114yes—
191C23×C4C23×C1112yes—
192C23×C4C23×C1111yescharacteristic
193C2×M16—42no—
194C2×M16—42no—
195C2×M16C2×C4×C1118yescomplemented
196C22×C8C23×C1114yes—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—44no—
200C2×C4⋊C4—44no—
201C2×C4⋊C4C23×C1114yes—
202C2×C4⋊C4C23×C1114yes—
203C2×C22⋊C4—24no—
204C2×C22⋊C4—24no—
205C2×C22⋊C4—48no—
206#107—44no—
207#106—44no—
208C22⋊C8C2×C4×C11116yescomplemented
209#95—24no—
210#95—24no—
211C2×C11—28no—
212C2×C11—42no—
213C2×C11#231511yescharacteristic
214C2×C11C2×#42812yes—
215C2×C11#319211yescharacteristic
216C2×C11#319312yes—
217C2×C11#319511yescharacteristic
218C24—24no—
219C24—24no—
220C24—41no—
221C24—41no—
222C24C11×C4⋊C414yes—
223C24C2×D4×C1111yescharacteristic
224C24C2×D4×C1112yes—
225C22×C4—24no—
226C22×C4—24no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—24no—
230C22×C4—24no—
231C22×C4—48no—
232C22×C4—48no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—44no—
238C22×C4—44no—
239C22×C4—44no—
240C22×C4—44no—
241C22×C4—44no—
242C22×C4—44no—
243C22×C4C11×C4⋊C414yes—
244C22×C4C11×C4⋊C418yes—
245C22×C4C22×C4×C1114yes—
246C22×C4C22×C4×C1112yes—
247C22×C4C2×D4×C1111yescharacteristic
248C22×C4C2×D4×C1112yes—
249C22×C4C2×Q8×C1112yes—
250C22×C4C2×Q8×C1114yes—
251C22×C4C24×C1111yescharacteristic
252M16—48no—
253C2×C8—24no—
254C2×C8—24no—
255C2×C8C22×C4×C1118yes—
256C4⋊C4—28no—
257C4⋊C4—28no—
258C4⋊C4—44no—
259C4⋊C4—44no—
260C22⋊C4—48no—
261C22⋊C4—48no—
262C11#2194211yescharacteristic, direct product factor, Sylow
263C23—22no—
264C23—22no—
265C23—22no—
266C23—22no—
267C23—21no—
268C23—21no—
269C23—216no—
270C23—22no—
271C23—22no—
272C23—44no—
273C23—44no—
274C23—48no—
275C23—44no—
276C23C2×C11×C4⋊C412yes—
277C23C2×C11×C4⋊C414yes—
278C23C11×AGL(1,ℤ/8)14yes—
279C23C11×#13714yes—
280C23C22×D4×C1111yescharacteristic
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—24no—
286C2×C4—28no—
287C2×C4—28no—
288C2×C4—24no—
289C2×C4—48no—
290C2×C4—44no—
291C2×C4—44no—
292C2×C4—44no—
293C2×C4—44no—
294C2×C4—44no—
295C2×C4—44no—
296C2×C4—44no—
297C2×C4—88no—
298C2×C4—88no—
299C2×C4C2×C11×C4⋊C414yes—
300C2×C4C2×C11×C4⋊C412yes—
301C2×C4C23×C4×C1111yescharacteristic
302C2×C4C22×Q8×C1111yescharacteristic
303C2×C4C11×H(5,𝔽2)12yes—
304C2×C4C11×H(5,𝔽2)12yes—
305C8—28no—
306C22—24no—
307C22—24no—
308C22—24no—
309C22—24no—
310C22—24no—
311C22—24no—
312C22—24no—
313C22—22no—
314C22—416no—
315C22—41no—
316C22—42no—
317C22—41no—
318C22C11×#42818yes—
319C22C22×C11×C4⋊C411yescharacteristic
320C22C11×#53411yescharacteristic
321C22C11×#53411yescharacteristic
322C22C2×C11×AGL(1,ℤ/8)12yes—
323C22C2×C11×#13712yes—
324C4—24no—
325C4—22no—
326C4—84no—
327C4—84no—
328C4C11×#51812yes—
329C4C11×#54312yes—
330C2—28no—
331C2—42no—
332C2C11×#231511yescharacteristic
333C2C2×C11×#42812yes—
334C2C11×#319211yescharacteristic
335C2C11×#319312yes—
336C2C11×#319511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC25×C11D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#1853C2semidirect
4. C11×#1852C2semidirect
5. C11×#1809C2semidirect
11. C2×C11×#107C22semidirect
12. C2×C11×#106C22semidirect
13. C11×#407C4semidirect
20. C11×#340C22semidirect
34. C2×C11×M16C2×C4semidirect
47. C11×C22⋊C8C2×C4semidirect
50. #21942C11direct (N × H)
97. #1853C2×C11semidirect
98. #1852C2×C11semidirect
99. #1809C2×C11semidirect
148. C2×#107C22×C11semidirect
149. C2×#106C22×C11semidirect
150. #407C4×C11semidirect
157. #340C22×C11semidirect
195. C2×M16C2×C4×C11semidirect
208. C22⋊C8C2×C4×C11semidirect
262. C11#21942direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4072
C2×C11×#3802
C11×#18532
C11×#18522
C11×#18092
#2194211