Finite Group Databasebeta

← C11×#21822 #14599015

Subgroups — C11×#21822 #14599015

Order 2816.

1242 conjugacy classes of subgroups.

The subgroup lattice has 236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C11C211yesmaximal, characteristic
2C2×C11×#432C212yesmaximal
3C11×#1985C218yesmaximal, complemented
4C11×#1817C214yesmaximal
5C23×Q8×C11C411yescharacteristic
6C2×C4×Q8×C11—28no—
7C2×C4×Q8×C11C414yes—
8C2×C4×Q8×C11C2214yes—
9C22×C11×C4⋊C4C411yescharacteristic
10C22×C11×C4⋊C4C412yes—
11C22×C42×C11C2212yes—
12C22×C42×C11C2211yescharacteristic
13C11×#432—28no—
14C2×C11×C4⋊C8C2214yes—
15C2×C11×C22⋊C8C2214yes—
16C2×C11×#97C2214yes—
17C11×#336C22116yes—
18C22×Q8×C11—24no—
19C22×Q8×C11—28no—
20C22×Q8×C11C2×C414yes—
21C23×C4×C11C2×C411yescharacteristic
22C23×C4×C11C2×C412yes—
23C23×C4×C11C2×C412yes—
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11C2311yescharacteristic
26C22×C8×C11C2318yes—
27C4×Q8×C11—216no—
28C4×Q8×C11—28no—
29C4×Q8×C11—28no—
30C2×C11×C4⋊C4—28no—
31C2×C11×C4⋊C4—24no—
32C2×C11×C4⋊C4C2×C414yes—
33C2×C11×C4⋊C4C2×C418yes—
34C2×C42×C11—28no—
35C2×C42×C11C2×C414yes—
36C2×C42×C11C2×C412yes—
37C2×C42×C11D418yes—
38C2×C42×C11C2314yes—
39C2×C42×C11C2312yes—
40C11×C4⋊C8—28no—
41C11×C22⋊C8—28no—
42C11×#97—28no—
43#21822C1111yesmaximal, characteristic, direct product factor, Sylow
44C24×C11C22×C411yescharacteristic
45C2×Q8×C11—232no—
46C2×Q8×C11—28no—
47C2×Q8×C11—216no—
48C22×C4×C11—24no—
49C22×C4×C11—24no—
50C22×C4×C11—24no—
51C22×C4×C11—24no—
52C22×C4×C11—24no—
53C22×C4×C11—42no—
54C22×C4×C11—44no—
55C22×C4×C11C22⋊C414yes—
56C22×C4×C11C22⋊C414yes—
57C22×C4×C11M1618yes—
58C22×C4×C11C22×C414yes—
59C22×C4×C11C22×C411yescharacteristic
60C22×C4×C11C22×C412yes—
61C22×C4×C11C22×C412yes—
62C22×C4×C11C22×C414yes—
63C22×C4×C11C2×D414yes—
64C22×C4×C11C2411yescharacteristic
65C2×C8×C11—28no—
66C2×C8×C11—216no—
67C11×C4⋊C4—216no—
68C11×C4⋊C4—28no—
69C42×C11—28no—
70C42×C11—28no—
71C42×C11C22⋊C418yes—
72C42×C11C2×D414yes—
73C42×C11C2×D414yes—
74C22×C4×Q8C2×C1111yescharacteristic
75C2×#432C2×C1112yes—
76#1985C2×C1118yescomplemented
77#1817C2×C1114yes—
78C23×C11—22no—
79C23×C11—22no—
80C23×C11C2×C22⋊C412yes—
81C23×C11C2×M1614yes—
82C23×C11C23×C411yescharacteristic
83Q8×C11—232no—
84C2×C4×C11—24no—
85C2×C4×C11—22no—
86C2×C4×C11—24no—
87C2×C4×C11—24no—
88C2×C4×C11—24no—
89C2×C4×C11—28no—
90C2×C4×C11—216no—
91C2×C4×C11—28no—
92C2×C4×C11—24no—
93C2×C4×C11—28no—
94C2×C4×C11—44no—
95C2×C4×C11—48no—
96C2×C4×C11C2×C22⋊C412yes—
97C2×C4×C11C2×C22⋊C414yes—
98C2×C4×C11C2×C22⋊C414yes—
99C2×C4×C11C2×M1618yes—
100C2×C4×C11C22×D412yes—
101C2×C4×C112−1+414yes—
102C8×C11—48no—
103C23×Q8C4×C1111yescharacteristic
104C2×C4×Q8—28no—
105C2×C4×Q8C4×C1114yes—
106C2×C4×Q8C22×C1114yes—
107C22×C4⋊C4C4×C1111yescharacteristic
108C22×C4⋊C4C4×C1112yes—
109C22×C42C22×C1112yes—
110C22×C42C22×C1111yescharacteristic
111#432—28no—
112C2×C4⋊C8C22×C1114yes—
113C2×C22⋊C8C22×C1114yes—
114C2×#97C22×C1114yes—
115#336C22×C11116yes—
116C22×C11—22no—
117C22×C11—22no—
118C22×C11—28no—
119C22×C11#40714yes—
120C22×C11C22×C22⋊C411yescharacteristic
121C22×C11#51912yes—
122C22×C11C22×M1612yes—
123C22×C11#56812yes—
124C4×C11—22no—
125C4×C11—24no—
126C4×C11—28no—
127C4×C11—24no—
128C4×C11—44no—
129C4×C11#53614yes—
130C22×Q8—24no—
131C22×Q8—28no—
132C22×Q8C2×C4×C1114yes—
133C23×C4C2×C4×C1111yescharacteristic
134C23×C4C2×C4×C1112yes—
135C23×C4C2×C4×C1112yes—
136C23×C4C2×C4×C1111yescharacteristic
137C23×C4C23×C1111yescharacteristic
138C22×C8C23×C1118yes—
139C4×Q8—216no—
140C4×Q8—28no—
141C4×Q8—28no—
142C2×C4⋊C4—28no—
143C2×C4⋊C4—24no—
144C2×C4⋊C4C2×C4×C1114yes—
145C2×C4⋊C4C2×C4×C1118yes—
146C2×C42—28no—
147C2×C42C2×C4×C1114yes—
148C2×C42C2×C4×C1112yes—
149C2×C42D4×C1118yes—
150C2×C42C23×C1114yes—
151C2×C42C23×C1112yes—
152C4⋊C8—28no—
153C22⋊C8—28no—
154#97—28no—
155C2×C11—24no—
156C2×C11#231011yescharacteristic
157C2×C11C2×#40711yescharacteristic
158C2×C11#287911yescharacteristic
159C2×C11#298314yes—
160C24C22×C4×C1111yescharacteristic
161C2×Q8—232no—
162C2×Q8—28no—
163C2×Q8—216no—
164C22×C4—24no—
165C22×C4—24no—
166C22×C4—24no—
167C22×C4—24no—
168C22×C4—24no—
169C22×C4—42no—
170C22×C4—44no—
171C22×C4C11×C22⋊C414yes—
172C22×C4C11×C22⋊C414yes—
173C22×C4C11×M1618yes—
174C22×C4C22×C4×C1114yes—
175C22×C4C22×C4×C1111yescharacteristic
176C22×C4C22×C4×C1112yes—
177C22×C4C22×C4×C1112yes—
178C22×C4C22×C4×C1114yes—
179C22×C4C2×D4×C1114yes—
180C22×C4C24×C1111yescharacteristic
181C2×C8—28no—
182C2×C8—216no—
183C4⋊C4—216no—
184C4⋊C4—28no—
185C42—28no—
186C42—28no—
187C42C11×C22⋊C418yes—
188C42C2×D4×C1114yes—
189C42C2×D4×C1114yes—
190C11#2182211yescharacteristic, direct product factor, Sylow
191C23—22no—
192C23—22no—
193C23C2×C11×C22⋊C412yes—
194C23C2×C11×M1614yes—
195C23C23×C4×C1111yescharacteristic
196Q8—232no—
197C2×C4—24no—
198C2×C4—22no—
199C2×C4—28no—
200C2×C4—216no—
201C2×C4—24no—
202C2×C4—24no—
203C2×C4—24no—
204C2×C4—28no—
205C2×C4—24no—
206C2×C4—28no—
207C2×C4—44no—
208C2×C4—48no—
209C2×C4C2×C11×C22⋊C412yes—
210C2×C4C2×C11×C22⋊C414yes—
211C2×C4C2×C11×C22⋊C414yes—
212C2×C4C2×C11×M1618yes—
213C2×C4C22×D4×C1112yes—
214C2×C4C11×2−1+414yes—
215C8—48no—
216C22—28no—
217C22—22no—
218C22—22no—
219C22C11×#40714yes—
220C22C22×C11×C22⋊C411yescharacteristic
221C22C11×#51912yes—
222C22C22×C11×M1612yes—
223C22C11×#56812yes—
224C4—22no—
225C4—24no—
226C4—28no—
227C4—24no—
228C4—44no—
229C4C11×#53614yes—
230C2—24no—
231C2C11×#231011yescharacteristic
232C2C2×C11×#40711yescharacteristic
233C2C11×#287911yescharacteristic
234C2C11×#298314yes—
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC24×C11C22×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#1985C2semidirect
43. #21822C11direct (N × H)
76. #1985C2×C11semidirect
190. C11#21822direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C112
C2×C11×#4322
C11×#19852
C11×#18172
#2182211