Finite Group Databasebeta

← C2×C11×#452 #13065839

Subgroups — C2×C11×#452 #13065839

Order 1408.

760 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#41C211yesmaximal, characteristic
2C22×C11×Q16C211yesmaximal, characteristic, complemented
3C22×C11×SD16C211yesmaximal, characteristic, complemented
4C2×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
5C11×#452C218yesmaximal, direct product factor
6C2×C11×#103C211yesmaximal, characteristic, complemented
7C2×C11×#102C211yesmaximal, characteristic, complemented
8C2×C11×C22⋊C8C211yesmaximal, characteristic, complemented
9C2×C11×#41—24no—
10C2×C11×#41—24no—
11C2×C11×#41—22no—
12C2×C11×#41C2214yes—
13C22×Q8×C11C2211yescharacteristic
14C22×Q8×C11C2211yescharacteristic
15C22×D4×C11—21no—
16C22×D4×C11C2211yescharacteristic
17C23×C4×C11—21no—
18C23×C4×C11C2211yescharacteristic
19C2×C11×Q16—24no—
20C2×C11×Q16C2214yescomplemented
21C2×C11×SD16—24no—
22C2×C11×SD16C2214yescomplemented
23C22×C8×C11C2211yescharacteristic
24C22×C8×C11C2211yescharacteristic
25C11×C22⋊Q8—22no—
26C11×C22⋊Q8C2214yescomplemented
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4C2211yescharacteristic
29C2×C11×C22⋊C4—21no—
30C11×#103C2214yescomplemented
31C11×#102C2214yescomplemented
32C11×C22⋊C8C2214yescomplemented
33C24×C11—21no—
34C24×C11D411yescharacteristic
35C11×#41—216no—
36C11×#41—28no—
37C11×#41—28no—
38C2×Q8×C11—22no—
39C2×Q8×C11—21no—
40C2×Q8×C11—21no—
41C2×Q8×C11—22no—
42C2×Q8×C11—22no—
43C2×Q8×C11D414yes—
44C2×Q8×C11C2312yes—
45C2×Q8×C11C2312yes—
46C2×D4×C11—28no—
47C2×D4×C11—24no—
48C2×D4×C11—21no—
49C2×D4×C11—22no—
50C2×D4×C11D414yes—
51C2×D4×C11C2312yes—
52C22×C4×C11—28no—
53C22×C4×C11—21no—
54C22×C4×C11—24no—
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11D412yes—
60C22×C4×C11D411yescharacteristic
61C22×C4×C11C2312yes—
62C22×C4×C11C2311yescharacteristic
63C11×Q16—28no—
64C11×SD16—28no—
65C2×C8×C11—22no—
66C2×C8×C11—22no—
67C2×C8×C11C2312yes—
68C2×C8×C11C2312yes—
69C11×C4⋊C4—24no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4C2312yes—
72C11×C22⋊C4—24no—
73C2×#452C1111yesmaximal, characteristic, direct product factor, Sylow
74C23×C11—22no—
75C23×C11—24no—
76C23×C11—22no—
77C23×C11—22no—
78C23×C11—22no—
79C23×C11—42no—
80C23×C11—42no—
81C23×C11C2×D412yes—
82C23×C11C2×D411yescharacteristic
83Q8×C11—24no—
84Q8×C11—22no—
85Q8×C11—22no—
86Q8×C11—22no—
87Q8×C11—42no—
88Q8×C11C2×D414yes—
89D4×C11—216no—
90D4×C11—24no—
91D4×C11—22no—
92D4×C11C2×D414yes—
93C2×C4×C11—216no—
94C2×C4×C11—22no—
95C2×C4×C11—24no—
96C2×C4×C11—22no—
97C2×C4×C11—24no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—42no—
103C2×C4×C11—42no—
104C2×C4×C11C2×D412yes—
105C2×C4×C11C2×D411yescharacteristic
106C2×C4×C11C2×D412yes—
107C2×C4×C11C2×D412yes—
108C2×C4×C11C2411yescharacteristic
109C8×C11—22no—
110C8×C11—22no—
111C22×#41C2×C1111yescharacteristic
112C22×Q16C2×C1111yescharacteristic, complemented
113C22×SD16C2×C1111yescharacteristic, complemented
114C2×C22⋊Q8C2×C1111yescharacteristic, complemented
115#452C2×C1118yesdirect product factor
116C2×#103C2×C1111yescharacteristic, complemented
117C2×#102C2×C1111yescharacteristic, complemented
118C2×C22⋊C8C2×C1111yescharacteristic, complemented
119C22×C11—22no—
120C22×C11—24no—
121C22×C11—22no—
122C22×C11—22no—
123C22×C11—42no—
124C22×C11—42no—
125C22×C11—44no—
126C22×C11—48no—
127C22×C11#12012yes—
128C22×C11#13512yes—
129C22×C11#13712yes—
130C22×C11C22×D411yescharacteristic
131C4×C11—22no—
132C4×C11—24no—
133C4×C11—42no—
134C4×C11—42no—
135C4×C11#12012yes—
136C4×C11C22×D411yescharacteristic
137C4×C11C22×D411yescharacteristic
138C2×#41—24no—
139C2×#41—24no—
140C2×#41—22no—
141C2×#41C22×C1114yes—
142C22×Q8C22×C1111yescharacteristic
143C22×Q8C22×C1111yescharacteristic
144C22×D4—21no—
145C22×D4C22×C1111yescharacteristic
146C23×C4—21no—
147C23×C4C22×C1111yescharacteristic
148C2×Q16—24no—
149C2×Q16C22×C1114yescomplemented
150C2×SD16—24no—
151C2×SD16C22×C1114yescomplemented
152C22×C8C22×C1111yescharacteristic
153C22×C8C22×C1111yescharacteristic
154C22⋊Q8—22no—
155C22⋊Q8C22×C1114yescomplemented
156C2×C4⋊C4—21no—
157C2×C4⋊C4C22×C1111yescharacteristic
158C2×C22⋊C4—21no—
159#103C22×C1114yescomplemented
160#102C22×C1114yescomplemented
161C22⋊C8C22×C1114yescomplemented
162C2×C11—42no—
163C2×C11—44no—
164C2×C11#45214yesdirect product factor
165C2×C11C2×#12011yescharacteristic
166C2×C11C2×#13511yescharacteristic
167C2×C11C2×#13711yescharacteristic
168C24—21no—
169C24D4×C1111yescharacteristic
170#41—216no—
171#41—28no—
172#41—28no—
173C2×Q8—22no—
174C2×Q8—21no—
175C2×Q8—21no—
176C2×Q8—22no—
177C2×Q8—22no—
178C2×Q8D4×C1114yes—
179C2×Q8C23×C1112yes—
180C2×Q8C23×C1112yes—
181C2×D4—28no—
182C2×D4—24no—
183C2×D4—21no—
184C2×D4—22no—
185C2×D4D4×C1114yes—
186C2×D4C23×C1112yes—
187C22×C4—28no—
188C22×C4—21no—
189C22×C4—24no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4D4×C1111yescharacteristic
195C22×C4D4×C1112yes—
196C22×C4C23×C1112yes—
197C22×C4C23×C1111yescharacteristic
198Q16—28no—
199SD16—28no—
200C2×C8—22no—
201C2×C8—22no—
202C2×C8C23×C1112yes—
203C2×C8C23×C1112yes—
204C4⋊C4—24no—
205C4⋊C4—21no—
206C4⋊C4C23×C1112yes—
207C22⋊C4—24no—
208C11C2×#45211yescharacteristic, direct product factor, Sylow
209C23—22no—
210C23—24no—
211C23—22no—
212C23—22no—
213C23—22no—
214C23—42no—
215C23—42no—
216C23C2×D4×C1112yes—
217C23C2×D4×C1111yescharacteristic
218Q8—24no—
219Q8—22no—
220Q8—22no—
221Q8—22no—
222Q8—42no—
223Q8C2×D4×C1114yes—
224D4—216no—
225D4—24no—
226D4—22no—
227D4C2×D4×C1114yes—
228C2×C4—216no—
229C2×C4—22no—
230C2×C4—24no—
231C2×C4—22no—
232C2×C4—24no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4C2×D4×C1112yes—
240C2×C4C2×D4×C1111yescharacteristic
241C2×C4C2×D4×C1112yes—
242C2×C4C2×D4×C1112yes—
243C2×C4C24×C1111yescharacteristic
244C8—22no—
245C8—22no—
246C22—22no—
247C22—24no—
248C22—22no—
249C22—22no—
250C22—42no—
251C22—42no—
252C22—44no—
253C22—48no—
254C22C11×#12012yes—
255C22C11×#13512yes—
256C22C11×#13712yes—
257C22C22×D4×C1111yescharacteristic
258C4—22no—
259C4—24no—
260C4—42no—
261C4—42no—
262C4C11×#12012yes—
263C4C22×D4×C1111yescharacteristic
264C4C22×D4×C1111yescharacteristic
265C2—42no—
266C2—44no—
267C2C11×#45214yesdirect product factor
268C2C2×C11×#12011yescharacteristic
269C2C2×C11×#13511yescharacteristic
270C2C2×C11×#13711yescharacteristic
subgroupG/H
center, socleC23×C11C2×D4
commutator, Frattini, cosocleC2×C4C24×C11
prime radicalC22×C11×#41C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×Q16C2semidirect
3. C22×C11×SD16C2semidirect
4. C2×C11×C22⋊Q8C2semidirect
5. C11×#452C2direct (N × H)
6. C2×C11×#103C2semidirect
7. C2×C11×#102C2semidirect
8. C2×C11×C22⋊C8C2semidirect
20. C2×C11×Q16C22semidirect
22. C2×C11×SD16C22semidirect
26. C11×C22⋊Q8C22semidirect
30. C11×#103C22semidirect
31. C11×#102C22semidirect
32. C11×C22⋊C8C22semidirect
73. C2×#452C11direct (N × H)
112. C22×Q16C2×C11semidirect
113. C22×SD16C2×C11semidirect
114. C2×C22⋊Q8C2×C11semidirect
115. #452C2×C11direct (N × H)
116. C2×#103C2×C11semidirect
117. C2×#102C2×C11semidirect
118. C2×C22⋊C8C2×C11semidirect
149. C2×Q16C22×C11semidirect
151. C2×SD16C22×C11semidirect
155. C22⋊Q8C22×C11semidirect
159. #103C22×C11semidirect
160. #102C22×C11semidirect
161. C22⋊C8C22×C11semidirect
164. C2×C11#452direct (N × H)
208. C11C2×#452direct (N × H)
267. C2C11×#452direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#412
C22×C11×Q162
C22×C11×SD162
C2×C11×C22⋊Q82
C11×#4522
C2×C11×#1032
C2×C11×#1022
C2×C11×C22⋊C82
C2×#45211