Finite Group Databasebeta

← #14647183

Subgroups — #14647183

Order 2816.

526 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 131 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
1#13068378C212yesmaximal
2#13066497C214yesmaximal, complemented
3C11×#2285C211yesmaximal, characteristic
4C2×C11×#117C412yes—
5C22×C42×C11C2211yescharacteristic
6C11×#384C411yescharacteristic
7C11×#384C411yescharacteristic
8C11×#382C2212yes—
9C11×#380—22no—
10C4×C11×C4⋊C4—22no—
11C2×C22⋊(C11⋊C8)—22no—
12C2×#66867C2214yes—
13#10622162—22no—
14C23×C4×C11C2×C411yescharacteristic
15C23×C4×C11D412yes—
16C11×#117—44no—
17C2×C11×C4⋊C4—22no—
18C2×C11×C4⋊C4—22no—
19C2×C11×C4⋊C4C2×C412yes—
20C2×C11×C4⋊C4C2×C412yes—
21C2×C11×C22⋊C4—22no—
22C2×C42×C11—24no—
23C2×C42×C11—22no—
24C2×C42×C11C2×C411yescharacteristic
25C2×C42×C11D412yes—
26C2×C42×C11C2311yescharacteristic
27C22×C11⋊C8—24no—
28C11×#95—24no—
29C22⋊(C11⋊C8)—28no—
30#66867—28no—
31#8721—111nomaximal, Sylow
32C24×C11C22⋊C411yescharacteristic
33C22×C4×C11—22no—
34C22×C4×C11—22no—
35C22×C4×C11—22no—
36C22×C4×C11—24no—
37C22×C4×C11—24no—
38C22×C4×C11—22no—
39C22×C4×C11—22no—
40C22×C4×C11—42no—
41C22×C4×C11C22⋊C411yescharacteristic
42C22×C4×C11C22⋊C412yes—
43C22×C4×C11C22×C411yescharacteristic
44C22×C4×C11C2×D412yes—
45C11×C4⋊C4—44no—
46C11×C4⋊C4—42no—
47C11×C4⋊C4—42no—
48C11×C4⋊C4—44no—
49C11×C22⋊C4—44no—
50C42×C11—22no—
51C42×C11—24no—
52C42×C11—44no—
53C42×C11#4114yes—
54C2×C11⋊C8—28no—
55C2×C11⋊C8—44no—
56C2×C11⋊C8—44no—
57#2285D1111yescharacteristic
58#1749—112no—
59#1295—114no—
60C23×C11—21no—
61C23×C11—21no—
62C23×C11—22no—
63C23×C11—22no—
64C23×C11#10112yes—
65C23×C11C2×C22⋊C411yescharacteristic
66C2×C4×C11—28no—
67C2×C4×C11—21no—
68C2×C4×C11—22no—
69C2×C4×C11—21no—
70C2×C4×C11—21no—
71C2×C4×C11—21no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—48no—
76C2×C4×C11—42no—
77C2×C4×C11—42no—
78C2×C4×C11—44no—
79C2×C4×C11—44no—
80C2×C4×C11#10012yes—
81C2×C4×C11#10414yes—
82C2×C4×C11#11712yes—
83C2×C4×C11#12314yes—
84C11⋊C8—48no—
85C2×#117Dic1112yes—
86C22×C42C2×D1111yescharacteristic
87C2×C22⋊C8—222no—
88C2×#97—114no—
89#384Dic1111yescharacteristic
90#384Dic1111yescharacteristic
91#382C2×D1112yes—
92#380—22no—
93C4×C4⋊C4—22no—
94#336—222no—
95C22×C11—22no—
96C22×C11—24no—
97C22×C11—41no—
98C22×C11—42no—
99C22×C11—41no—
100C22×C11#38111yescharacteristic
101C22×C11C2×#10011yescharacteristic
102C22×C11C2×#10111yescharacteristic
103C22×C11C2×#10412yes—
104C22×C11#42112yes—
105C4×C11—22no—
106C4×C11—22no—
107C4×C11—24no—
108C4×C11—24no—
109C4×C11—82no—
110C4×C11—82no—
111C23×C4C2×Dic1111yescharacteristic
112C23×C4C22⋊D1112yes—
113C22×C8—224no—
114#117—44no—
115C2×C4⋊C4—22no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4C2×Dic1112yes—
118C2×C4⋊C4C2×Dic1112yes—
119C2×C22⋊C4—22no—
120C2×C42—24no—
121C2×C42—22no—
122C2×C42C2×Dic1111yescharacteristic
123C2×C42C22⋊D1112yes—
124C2×C42C22×D1111yescharacteristic
125C22⋊C8—228no—
126#97—228no—
127#95—24no—
128C2×C11—42no—
129C2×C11#152511yescharacteristic
130C2×C11#153112yes—
131C2×C11#153611yescharacteristic
132C2×C11#182111yescharacteristic
133C2×C11#182612yes—
134C24C22⋊Dic1111yescharacteristic
135C22×C4—22no—
136C22×C4—22no—
137C22×C4—22no—
138C22×C4—24no—
139C22×C4—24no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—42no—
143C22×C4C22⋊Dic1111yescharacteristic
144C22×C4C22⋊Dic1112yes—
145C22×C4C22×Dic1111yescharacteristic
146C22×C4C2×C22⋊D1112yes—
147C2×C8—228no—
148C2×C8—444no—
149C2×C8—444no—
150C4⋊C4—42no—
151C4⋊C4—42no—
152C4⋊C4—44no—
153C4⋊C4—44no—
154C22⋊C4—44no—
155C42—22no—
156C42—24no—
157C42—44no—
158C42#433914yes—
159C11#872111yescharacteristic, complemented, Sylow
160C23—21no—
161C23—21no—
162C23—22no—
163C23—22no—
164C23#6690012yes—
165C23C2×C22⋊Dic1111yescharacteristic
166C2×C4—28no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—48no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—44no—
179C2×C4—44no—
180C2×C4#6689712yes—
181C2×C4#6690114yes—
182C2×C4#6697912yes—
183C2×C4#6698214yes—
184C8—448no—
185C22—22no—
186C22—24no—
187C22—42no—
188C22—41no—
189C22—41no—
190C22#1062282411yescharacteristic
191C22C2×#6689711yescharacteristic
192C22C2×#6690011yescharacteristic
193C22C2×#6690112yes—
194C22#1062284912yes—
195C4—22no—
196C4—22no—
197C4—24no—
198C4—24no—
199C4—82no—
200C4—82no—
201C2—42no—
202C2#1306720811yescharacteristic
203C2#1306723112yes—
204C2#1306725111yescharacteristic
205C2#1306869611yescharacteristic
206C2#1306871512yes—
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2285C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2285D11
hypocenterC11#8721
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2285

Complements

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

NH ≅ G/Ntype
2. #13066497C2semidirect
159. C11#8721semidirect

Maximal subgroups

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

subgroupindex
#130683782
#130664972
C11×#22852
#872111