Finite Group Databasebeta

← C11×#11511 #14588704

Subgroups — C11×#11511 #14588704

Order 2816.

490 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#382C211yesmaximal, characteristic
2C11×#1463C212yesmaximal
3C11×#1324C214yesmaximal, complemented
4C22×C11×C4⋊C4C411yescharacteristic
5C22×C11×C4⋊C4C2211yescharacteristic
6C22×C42×C11C411yescharacteristic
7C11×#407—22no—
8C11×#382—22no—
9C11×#382C412yes—
10C11×#382C2212yes—
11C2×C11×#95—22no—
12C11×#324—22no—
13C11×#324C2214yes—
14C23×C4×C11—21no—
15C23×C4×C11—21no—
16C23×C4×C11C2×C411yescharacteristic
17C23×C4×C11D412yes—
18C2×C11×M16—42no—
19C2×C11×C4⋊C4—21no—
20C2×C11×C4⋊C4—41no—
21C2×C11×C4⋊C4—41no—
22C2×C11×C4⋊C4—41no—
23C2×C11×C4⋊C4—41no—
24C2×C11×C4⋊C4C2×C412yes—
25C2×C11×C4⋊C4C2×C411yescharacteristic
26C2×C11×C4⋊C4D412yes—
27C2×C11×C4⋊C4C2311yescharacteristic
28C2×C42×C11—21no—
29C2×C42×C11—24no—
30C2×C42×C11C2×C412yes—
31C11×C22⋊C8—24no—
32C11×C22⋊C8—42no—
33C11×#95—24no—
34C11×#95—24no—
35#11511C1111yesmaximal, characteristic, direct product factor, Sylow
36C24×C11C22⋊C411yescharacteristic
37C22×C4×C11—21no—
38C22×C4×C11—21no—
39C22×C4×C11—22no—
40C22×C4×C11—22no—
41C22×C4×C11—24no—
42C22×C4×C11—22no—
43C22×C4×C11—22no—
44C22×C4×C11—22no—
45C22×C4×C11—22no—
46C22×C4×C11—42no—
47C22×C4×C11—42no—
48C22×C4×C11—44no—
49C22×C4×C11—44no—
50C22×C4×C11—41no—
51C22×C4×C11—41no—
52C22×C4×C11C22⋊C411yescharacteristic
53C22×C4×C11C22⋊C412yes—
54C22×C4×C11C22×C411yescharacteristic
55C22×C4×C11C2×D412yes—
56C11×M16—84no—
57C2×C8×C11—44no—
58C11×C4⋊C4—41no—
59C11×C4⋊C4—42no—
60C11×C4⋊C4—41no—
61C11×C4⋊C4—42no—
62C11×C4⋊C4—42no—
63C42×C11—24no—
64C42×C11—22no—
65C42×C11M1614yescomplemented
66C2×#382C2×C1111yescharacteristic
67#1463C2×C1112yes—
68#1324C2×C1114yescomplemented
69C23×C11—22no—
70C23×C11—22no—
71C23×C11—21no—
72C23×C11—21no—
73C23×C11#9911yescharacteristic
74C23×C11#9911yescharacteristic
75C23×C11C2×C22⋊C411yescharacteristic
76C2×C4×C11—24no—
77C2×C4×C11—24no—
78C2×C4×C11—21no—
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11—21no—
82C2×C4×C11—24no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—48no—
86C2×C4×C11—42no—
87C2×C4×C11—42no—
88C2×C4×C11—44no—
89C2×C4×C11—42no—
90C2×C4×C11—42no—
91C2×C4×C11—44no—
92C2×C4×C11—42no—
93C2×C4×C11—82no—
94C2×C4×C11—82no—
95C2×C4×C11—82no—
96C2×C4×C11#10112yes—
97C2×C4×C11C2×M1612yes—
98C8×C11—84no—
99C22×C4⋊C4C4×C1111yescharacteristic
100C22×C4⋊C4C22×C1111yescharacteristic
101C22×C42C4×C1111yescharacteristic
102#407—22no—
103#382—22no—
104#382C4×C1112yes—
105#382C22×C1112yes—
106C2×#95—22no—
107#324—22no—
108#324C22×C1114yes—
109C22×C11—24no—
110C22×C11—24no—
111C22×C11—21no—
112C22×C11—21no—
113C22×C11—21no—
114C22×C11—21no—
115C22×C11—21no—
116C22×C11—21no—
117C22×C11#35412yes—
118C22×C11#35512yes—
119C22×C11#40711yescharacteristic
120C22×C11C2×#9911yescharacteristic
121C22×C11C2×#10111yescharacteristic
122C4×C11—22no—
123C4×C11—22no—
124C4×C11—44no—
125C4×C11—42no—
126C4×C11—42no—
127C4×C11—82no—
128C23×C4—21no—
129C23×C4—21no—
130C23×C4C2×C4×C1111yescharacteristic
131C23×C4D4×C1112yes—
132C2×M16—42no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—41no—
135C2×C4⋊C4—41no—
136C2×C4⋊C4—41no—
137C2×C4⋊C4—41no—
138C2×C4⋊C4C2×C4×C1112yes—
139C2×C4⋊C4C2×C4×C1111yescharacteristic
140C2×C4⋊C4D4×C1112yes—
141C2×C4⋊C4C23×C1111yescharacteristic
142C2×C42—21no—
143C2×C42—24no—
144C2×C42C2×C4×C1112yes—
145C22⋊C8—24no—
146C22⋊C8—42no—
147#95—24no—
148#95—24no—
149C2×C11—21no—
150C2×C11—22no—
151C2×C11—22no—
152C2×C11—21no—
153C2×C11#146311yescharacteristic
154C2×C11C2×#35411yescharacteristic
155C2×C11C2×#35511yescharacteristic
156C24C11×C22⋊C411yescharacteristic
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—24no—
162C22×C4—22no—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4—22no—
166C22×C4—42no—
167C22×C4—42no—
168C22×C4—44no—
169C22×C4—44no—
170C22×C4—41no—
171C22×C4—41no—
172C22×C4C11×C22⋊C411yescharacteristic
173C22×C4C11×C22⋊C412yes—
174C22×C4C22×C4×C1111yescharacteristic
175C22×C4C2×D4×C1112yes—
176M16—84no—
177C2×C8—44no—
178C4⋊C4—41no—
179C4⋊C4—42no—
180C4⋊C4—41no—
181C4⋊C4—42no—
182C4⋊C4—42no—
183C42—24no—
184C42—22no—
185C42C11×M1614yescomplemented
186C11#1151111yescharacteristic, direct product factor, Sylow
187C23—22no—
188C23—22no—
189C23—21no—
190C23—21no—
191C23C11×#9911yescharacteristic
192C23C11×#9911yescharacteristic
193C23C2×C11×C22⋊C411yescharacteristic
194C2×C4—24no—
195C2×C4—24no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—24no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—48no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—44no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—44no—
210C2×C4—42no—
211C2×C4—82no—
212C2×C4—82no—
213C2×C4—82no—
214C2×C4C11×#10112yes—
215C2×C4C2×C11×M1612yes—
216C8—84no—
217C22—24no—
218C22—24no—
219C22—21no—
220C22—21no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22C11×#35412yes—
226C22C11×#35512yes—
227C22C11×#40711yescharacteristic
228C22C2×C11×#9911yescharacteristic
229C22C2×C11×#10111yescharacteristic
230C4—22no—
231C4—22no—
232C4—44no—
233C4—42no—
234C4—42no—
235C4—82no—
236C2—21no—
237C2—22no—
238C2—22no—
239C2—21no—
240C2C11×#146311yescharacteristic
241C2C2×C11×#35411yescharacteristic
242C2C2×C11×#35511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC24×C11C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C24×C11 ◁ C22×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#1324C2semidirect
35. #11511C11direct (N × H)
65. C42×C11M16semidirect
68. #1324C2×C11semidirect
185. C42C11×M16semidirect
186. C11#11511direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3822
C11×#14632
C11×#13242
#1151111