Finite Group Databasebeta

← C11×#23347 #14600540

Subgroups — C11×#23347 #14600540

Order 2816.

752 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C11×#124C211yesmaximal, characteristic
2C11×#1984C212yesmaximal, complemented
3C11×#1923C214yesmaximal, complemented
4C11×#1870C212yesmaximal
5C11×#1851C214yesmaximal, complemented
6C11×#1831C212yesmaximal, complemented
7C22×C11×M16C2212yes—
8C2×C11×#124C411yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C2×C11×C4⋊C8C2212yes—
12C2×C11×C4⋊C8C2212yes—
13C2×C11×C4⋊C8C2212yes—
14C2×C11×C22⋊C8C2212yes—
15C2×C11×C22⋊C8C2214yes—
16C2×C4×C8×C11C2212yes—
17C11×#391C411yescharacteristic
18C11×#390C411yescharacteristic
19C11×#388C414yes—
20C11×#382C411yescharacteristic
21C4×C11×C22⋊C4C2214yes—
22C43×C11C2211yescharacteristic
23C11×#336C2214yes—
24C11×#336C2214yes—
25C11×#336C2214yes—
26C22×Q8×C11C2×C411yescharacteristic
27C22×D4×C11C2×C411yescharacteristic
28C23×C4×C11C2312yes—
29C2×C11×M16—44no—
30C2×C11×M16—42no—
31C22×C8×C11C2314yes—
32C22×C8×C11C2314yes—
33C11×#124—24no—
34C4×Q8×C11—41no—
35C4×Q8×C11—41no—
36C4×D4×C11—41no—
37C4×D4×C11—41no—
38C2×C11×C4⋊C4C2×C411yescharacteristic
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C4⋊C4C2×C412yes—
41C2×C11×C22⋊C4C2×C414yes—
42C2×C11×C22⋊C4C2×C414yes—
43C2×C11×C22⋊C4C2×C412yes—
44C2×C42×C11C2×C411yescharacteristic
45C2×C42×C11C2×C412yes—
46C2×C42×C11C2×C411yescharacteristic
47C2×C42×C11C2311yescharacteristic
48C2×C42×C11C2312yes—
49C2×C42×C11C2312yes—
50C11×C4⋊C8—42no—
51C11×C4⋊C8—42no—
52C11×C4⋊C8—42no—
53C11×C22⋊C8—42no—
54C11×C22⋊C8—44no—
55C4×C8×C11—42no—
56C11×#95C2×C414yes—
57C11×#95C2×C414yes—
58#23347C1111yesmaximal, characteristic, direct product factor, Sylow
59C24×C11C22×C412yes—
60C2×Q8×C11—41no—
61C2×Q8×C11—41no—
62C2×Q8×C11M1614yescomplemented
63C2×D4×C11—22no—
64C2×D4×C11—41no—
65C2×D4×C11—41no—
66C22×C4×C11—22no—
67C22×C4×C11—24no—
68C22×C4×C11—22no—
69C22×C4×C11—24no—
70C22×C4×C11C22×C412yes—
71C22×C4×C11C22×C412yes—
72C22×C4×C11C22×C412yes—
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C22×C412yes—
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C22×C412yes—
77C22×C4×C11C2411yescharacteristic
78C11×M16—48no—
79C2×C8×C11—24no—
80C2×C8×C11—24no—
81C2×C8×C11—24no—
82C2×C8×C11—24no—
83C2×C8×C11—24no—
84C2×C8×C11—24no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—42no—
88C11×C22⋊C4—28no—
89C11×C22⋊C4—28no—
90C11×C22⋊C4—42no—
91C42×C11—22no—
92C42×C11—24no—
93C42×C11—22no—
94C42×C11—22no—
95C42×C11—22no—
96C42×C11—21no—
97C42×C11—21no—
98C42×C11—22no—
99C42×C11—41no—
100C4×#124C2×C1111yescharacteristic
101#1984C2×C1112yescomplemented
102#1923C2×C1114yescomplemented
103#1870C2×C1112yes—
104#1851C2×C1114yescomplemented
105#1831C2×C1112yescomplemented
106C23×C11—22no—
107C23×C11—24no—
108C23×C11—22no—
109C23×C11—24no—
110C23×C11—22no—
111C23×C11C23×C411yescharacteristic
112Q8×C11—44no—
113D4×C11—44no—
114C2×C4×C11—21no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—22no—
118C2×C4×C11—21no—
119C2×C4×C11—22no—
120C2×C4×C11—21no—
121C2×C4×C11—22no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—24no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—24no—
129C2×C4×C11—42no—
130C2×C4×C11—44no—
131C2×C4×C11—42no—
132C2×C4×C11C2×M1612yes—
133C2×C4×C11C2×M1614yes—
134C2×C4×C11#13114yes—
135C2×C4×C11H(5,𝔽2)12yes—
136C2×C4×C11H(5,𝔽2)11yescharacteristic
137C2×C4×C11H(5,𝔽2)11yescharacteristic
138C2×C4×C112−1+412yes—
139C8×C11—44no—
140C8×C11—44no—
141C22×M16C22×C1112yes—
142C2×#124C4×C1111yescharacteristic
143C2×C4×Q8C22×C1111yescharacteristic
144C2×C4×D4C22×C1111yescharacteristic
145C2×C4⋊C8C22×C1112yes—
146C2×C4⋊C8C22×C1112yes—
147C2×C4⋊C8C22×C1112yes—
148C2×C22⋊C8C22×C1114yes—
149C2×C22⋊C8C22×C1112yes—
150C2×C4×C8C22×C1112yes—
151#391C4×C1111yescharacteristic
152#390C4×C1111yescharacteristic
153#388C4×C1114yes—
154#382C4×C1111yescharacteristic
155C4×C22⋊C4C22×C1114yes—
156C43C22×C1111yescharacteristic
157#336C22×C1114yes—
158#336C22×C1114yes—
159#336C22×C1114yes—
160C22×C11—42no—
161C22×C11—42no—
162C22×C11—42no—
163C22×C11—44no—
164C22×C11—44no—
165C22×C11#51811yescharacteristic
166C22×C11#52012yes—
167C22×C11C22×M1611yescharacteristic
168C22×C11C2×#13112yes—
169C22×C11#56811yescharacteristic
170C4×C11—22no—
171C4×C11—24no—
172C4×C11—24no—
173C4×C11—42no—
174C4×C11—41no—
175C4×C11—42no—
176C4×C11—42no—
177C4×C11H(3,𝔽4)11yescharacteristic
178C4×C11#56212yes—
179C4×C11#56311yescharacteristic
180C22×Q8C2×C4×C1111yescharacteristic
181C22×D4C2×C4×C1111yescharacteristic
182C23×C4C23×C1112yes—
183C2×M16—44no—
184C2×M16—42no—
185C22×C8C23×C1114yes—
186C22×C8C23×C1114yes—
187#124—24no—
188C4×Q8—41no—
189C4×Q8—41no—
190C4×D4—41no—
191C4×D4—41no—
192C2×C4⋊C4C2×C4×C1111yescharacteristic
193C2×C4⋊C4C2×C4×C1111yescharacteristic
194C2×C4⋊C4C2×C4×C1112yes—
195C2×C22⋊C4C2×C4×C1114yes—
196C2×C22⋊C4C2×C4×C1114yes—
197C2×C22⋊C4C2×C4×C1112yes—
198C2×C42C2×C4×C1111yescharacteristic
199C2×C42C2×C4×C1112yes—
200C2×C42C2×C4×C1111yescharacteristic
201C2×C42C23×C1111yescharacteristic
202C2×C42C23×C1112yes—
203C2×C42C23×C1112yes—
204C4⋊C8—42no—
205C4⋊C8—42no—
206C4⋊C8—42no—
207C22⋊C8—42no—
208C22⋊C8—44no—
209C4×C8—42no—
210#95C2×C4×C1114yes—
211#95C2×C4×C1114yes—
212C2×C11—82no—
213C2×C11#237911yescharacteristic
214C2×C11#297311yescharacteristic
215C2×C11#297911yescharacteristic
216C2×C11#299112yes—
217C2×C11#299212yes—
218C24C22×C4×C1112yes—
219C2×Q8—41no—
220C2×Q8—41no—
221C2×Q8C11×M1614yescomplemented
222C2×D4—22no—
223C2×D4—41no—
224C2×D4—41no—
225C22×C4—22no—
226C22×C4—24no—
227C22×C4—22no—
228C22×C4—24no—
229C22×C4C22×C4×C1112yes—
230C22×C4C22×C4×C1112yes—
231C22×C4C22×C4×C1112yes—
232C22×C4C22×C4×C1111yescharacteristic
233C22×C4C22×C4×C1112yes—
234C22×C4C22×C4×C1111yescharacteristic
235C22×C4C22×C4×C1112yes—
236C22×C4C24×C1111yescharacteristic
237M16—48no—
238C2×C8—24no—
239C2×C8—24no—
240C2×C8—24no—
241C2×C8—24no—
242C2×C8—24no—
243C2×C8—24no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—42no—
247C22⋊C4—28no—
248C22⋊C4—28no—
249C22⋊C4—42no—
250C42—22no—
251C42—24no—
252C42—22no—
253C42—22no—
254C42—22no—
255C42—21no—
256C42—21no—
257C42—22no—
258C42—41no—
259C11#2334711yescharacteristic, direct product factor, Sylow
260C23—22no—
261C23—24no—
262C23—22no—
263C23—24no—
264C23—22no—
265C23C23×C4×C1111yescharacteristic
266Q8—44no—
267D4—44no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—24no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—24no—
283C2×C4—42no—
284C2×C4—44no—
285C2×C4—42no—
286C2×C4C2×C11×M1612yes—
287C2×C4C2×C11×M1614yes—
288C2×C4C11×#13114yes—
289C2×C4C11×H(5,𝔽2)12yes—
290C2×C4C11×H(5,𝔽2)11yescharacteristic
291C2×C4C11×H(5,𝔽2)11yescharacteristic
292C2×C4C11×2−1+412yes—
293C8—44no—
294C8—44no—
295C22—42no—
296C22—42no—
297C22—42no—
298C22—44no—
299C22—44no—
300C22C11×#51811yescharacteristic
301C22C11×#52012yes—
302C22C22×C11×M1611yescharacteristic
303C22C2×C11×#13112yes—
304C22C11×#56811yescharacteristic
305C4—22no—
306C4—24no—
307C4—24no—
308C4—42no—
309C4—41no—
310C4—42no—
311C4—42no—
312C4C11×H(3,𝔽4)11yescharacteristic
313C4C11×#56212yes—
314C4C11×#56311yescharacteristic
315C2—82no—
316C2C11×#237911yescharacteristic
317C2C11×#297311yescharacteristic
318C2C11×#297911yescharacteristic
319C2C11×#299112yes—
320C2C11×#299212yes—
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC22×D4×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×#1984C2semidirect
3. C11×#1923C2semidirect
5. C11×#1851C2semidirect
6. C11×#1831C2semidirect
58. #23347C11direct (N × H)
62. C2×Q8×C11M16semidirect
101. #1984C2×C11semidirect
102. #1923C2×C11semidirect
104. #1851C2×C11semidirect
105. #1831C2×C11semidirect
221. C2×Q8C11×M16semidirect
259. C11#23347direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C11×#1242
C11×#19842
C11×#19232
C11×#18702
C11×#18512
C11×#18312
#2334711