Finite Group Databasebeta

← C11×#21830 #14599023

Subgroups — C11×#21830 #14599023

Order 2816.

978 conjugacy classes of subgroups.

The subgroup lattice has 214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#125C211yesmaximal, characteristic
2C11×#2920C212yesmaximal
3C11×#1998C218yesmaximal, complemented
4C11×#1821C214yesmaximal
5C2×C11×#125—24no—
6C2×C11×#125—24no—
7C2×C11×#125C414yes—
8C2×C11×#125C2214yes—
9C22×C11×C4⋊C4C414yes—
10C22×C11×C4⋊C4C2212yes—
11C22×C42×C11C2211yescharacteristic
12C11×#432—24no—
13C11×#431—24no—
14C11×#423C2214yes—
15C11×#407C2214yes—
16C4×C11×M16C2214yes—
17C11×#343C22116yes—
18C23×C4×C11C2×C414yes—
19C23×C4×C11C2×C412yes—
20C23×C4×C11C2311yescharacteristic
21C2×C11×M16C2318yes—
22C11×#125—24no—
23C11×#125—28no—
24C11×#125—24no—
25C11×#125—24no—
26C11×#125—24no—
27C11×#125—28no—
28C2×C11×C4⋊C4—28no—
29C2×C11×C4⋊C4—24no—
30C2×C11×C4⋊C4—24no—
31C2×C11×C4⋊C4—24no—
32C2×C11×C4⋊C4—24no—
33C2×C11×C4⋊C4C2×C4116yes—
34C2×C11×C4⋊C4C2×C414yes—
35C2×C11×C4⋊C4C2314yes—
36C2×C42×C11C2×C412yes—
37C2×C42×C11D414yes—
38C2×C42×C11D414yes—
39C2×C42×C11C2312yes—
40C11×C4⋊C8—28no—
41C11×C22⋊C8—28no—
42C11×#97—24no—
43C4×C8×C11—24no—
44#21830C1111yesmaximal, characteristic, direct product factor, Sylow
45C24×C11C22×C411yescharacteristic
46C22×C4×C11—24no—
47C22×C4×C11—24no—
48C22×C4×C11—24no—
49C22×C4×C11—44no—
50C22×C4×C11—48no—
51C22×C4×C11C22⋊C414yes—
52C22×C4×C11C22⋊C412yes—
53C22×C4×C11C22⋊C412yes—
54C22×C4×C11C22×C411yescharacteristic
55C22×C4×C11C22×C418yes—
56C22×C4×C11C22×C414yes—
57C22×C4×C11C2×D414yes—
58C22×C4×C11C2411yescharacteristic
59C11×M16—216no—
60C2×C8×C11—28no—
61C11×C4⋊C4—28no—
62C11×C4⋊C4—216no—
63C11×C4⋊C4—216no—
64C11×C4⋊C4—28no—
65C42×C11C22⋊C412yes—
66C42×C11C22⋊C414yes—
67C42×C11C22⋊C412yes—
68C42×C11C2×D412yes—
69C42×C11C2×D412yes—
70C42×C11C2×D414yes—
71C22×#125C2×C1111yescharacteristic
72#2920C2×C1112yes—
73#1998C2×C1118yescomplemented
74#1821C2×C1114yes—
75C23×C11—22no—
76C23×C11—24no—
77C23×C11C2×C22⋊C412yes—
78C23×C11C23×C411yescharacteristic
79C2×C4×C11—22no—
80C2×C4×C11—28no—
81C2×C4×C11—28no—
82C2×C4×C11—28no—
83C2×C4×C11—42no—
84C2×C4×C11—42no—
85C2×C4×C11—44no—
86C2×C4×C11—48no—
87C2×C4×C11—48no—
88C2×C4×C11—48no—
89C2×C4×C11C2×C22⋊C412yes—
90C2×C4×C11C2×C22⋊C414yes—
91C2×C4×C11C2×C22⋊C414yes—
92C2×C4×C11C22×D412yes—
93C2×C4×C112−1+414yes—
94C8×C11—48no—
95C2×#125—24no—
96C2×#125—24no—
97C2×#125C4×C1114yes—
98C2×#125C22×C1114yes—
99C22×C4⋊C4C4×C1114yes—
100C22×C4⋊C4C22×C1112yes—
101C22×C42C22×C1111yescharacteristic
102#432—24no—
103#431—24no—
104#423C22×C1114yes—
105#407C22×C1114yes—
106C4×M16C22×C1114yes—
107#343C22×C11116yes—
108C22×C11—28no—
109C22×C11—22no—
110C22×C11—22no—
111C22×C11—22no—
112C22×C11#41314yes—
113C22×C11C22×C22⋊C411yescharacteristic
114C22×C11#51912yes—
115C4×C11—22no—
116C4×C11—24no—
117C4×C11—24no—
118C4×C11—48no—
119C4×C11#53614yes—
120C23×C4C2×C4×C1114yes—
121C23×C4C2×C4×C1112yes—
122C23×C4C23×C1111yescharacteristic
123C2×M16C23×C1118yes—
124#125—24no—
125#125—28no—
126#125—24no—
127#125—24no—
128#125—24no—
129#125—28no—
130C2×C4⋊C4—28no—
131C2×C4⋊C4—24no—
132C2×C4⋊C4—24no—
133C2×C4⋊C4—24no—
134C2×C4⋊C4—24no—
135C2×C4⋊C4C2×C4×C11116yes—
136C2×C4⋊C4C2×C4×C1114yes—
137C2×C4⋊C4C23×C1114yes—
138C2×C42C2×C4×C1112yes—
139C2×C42D4×C1114yes—
140C2×C42D4×C1114yes—
141C2×C42C23×C1112yes—
142C4⋊C8—28no—
143C22⋊C8—28no—
144#97—24no—
145C4×C8—24no—
146C2×C11—22no—
147C2×C11—24no—
148C2×C11#231011yescharacteristic
149C2×C11C2×#41312yes—
150C24C22×C4×C1111yescharacteristic
151C22×C4—24no—
152C22×C4—24no—
153C22×C4—24no—
154C22×C4—44no—
155C22×C4—48no—
156C22×C4C11×C22⋊C414yes—
157C22×C4C11×C22⋊C412yes—
158C22×C4C11×C22⋊C412yes—
159C22×C4C22×C4×C1111yescharacteristic
160C22×C4C22×C4×C1118yes—
161C22×C4C22×C4×C1114yes—
162C22×C4C2×D4×C1114yes—
163C22×C4C24×C1111yescharacteristic
164M16—216no—
165C2×C8—28no—
166C4⋊C4—28no—
167C4⋊C4—216no—
168C4⋊C4—216no—
169C4⋊C4—28no—
170C42C11×C22⋊C412yes—
171C42C11×C22⋊C414yes—
172C42C11×C22⋊C412yes—
173C42C2×D4×C1112yes—
174C42C2×D4×C1112yes—
175C42C2×D4×C1114yes—
176C11#2183011yescharacteristic, direct product factor, Sylow
177C23—22no—
178C23—24no—
179C23C2×C11×C22⋊C412yes—
180C23C23×C4×C1111yescharacteristic
181C2×C4—22no—
182C2×C4—28no—
183C2×C4—28no—
184C2×C4—28no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—44no—
188C2×C4—48no—
189C2×C4—48no—
190C2×C4—48no—
191C2×C4C2×C11×C22⋊C412yes—
192C2×C4C2×C11×C22⋊C414yes—
193C2×C4C2×C11×C22⋊C414yes—
194C2×C4C22×D4×C1112yes—
195C2×C4C11×2−1+414yes—
196C8—48no—
197C22—28no—
198C22—22no—
199C22—22no—
200C22—22no—
201C22C11×#41314yes—
202C22C22×C11×C22⋊C411yescharacteristic
203C22C11×#51912yes—
204C4—22no—
205C4—24no—
206C4—24no—
207C4—48no—
208C4C11×#53614yes—
209C2—22no—
210C2—24no—
211C2C11×#231011yescharacteristic
212C2C2×C11×#41312yes—
subgroupG/H
center, socleC22×C11C22×C22⋊C4
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#1998C2semidirect
44. #21830C11direct (N × H)
73. #1998C2×C11semidirect
176. C11#21830direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1252
C11×#29202
C11×#19982
C11×#18212
#2183011