Finite Group Databasebeta

← #14763238

Subgroups — #14763238

Order 2816.

978 conjugacy classes of subgroups; only the 323 normal subgroups are shown.

normal subgroups only

This group has 978 conjugacy classes of subgroups — too many to draw. Only its 323 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#13077249C212yesmaximal
2#13069610C218yesmaximal, complemented
3#13068696C214yesmaximal
4C22×C11×#125C211yesmaximal, characteristic
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
12#10622820C2214yes—
13#10622539—24no—
14#10622538—24no—
15#10622537C2214yes—
16C4×#4318C2214yes—
17#10622168C22116yes—
18C23×C4×C11C2×C414yes—
19C23×C4×C11C2×C412yes—
20C23×C4×C11C2311yescharacteristic
21C11×#125—24no—
22C11×#125—28no—
23C11×#125—24no—
24C11×#125—24no—
25C11×#125—24no—
26C11×#125—28no—
27C2×C11×C4⋊C4—28no—
28C2×C11×C4⋊C4—24no—
29C2×C11×C4⋊C4—24no—
30C2×C11×C4⋊C4—24no—
31C2×C11×C4⋊C4—24no—
32C2×C11×C4⋊C4C2×C4116yes—
33C2×C11×C4⋊C4C2×C414yes—
34C2×C11×C4⋊C4C2314yes—
35C2×C42×C11C2×C412yes—
36C2×C42×C11D414yes—
37C2×C42×C11D414yes—
38C2×C42×C11C2312yes—
39C2×#4318C2318yes—
40C22⋊(C11⋊C8)—28no—
41C4⋊(C11⋊C8)—28no—
42#66867—24no—
43C4×C11⋊C8—24no—
44#21830—111nomaximal, 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×C4⋊C4—28no—
60C11×C4⋊C4—216no—
61C11×C4⋊C4—216no—
62C11×C4⋊C4—28no—
63C42×C11C22⋊C412yes—
64C42×C11C22⋊C414yes—
65C42×C11C22⋊C412yes—
66C42×C11C2×D412yes—
67C42×C11C2×D412yes—
68C42×C11C2×D414yes—
69#4318—216no—
70C2×C11⋊C8—28no—
71C22×#125D1111yescharacteristic
72#2920—112no—
73#1998—118no—
74#1821—114no—
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—
94C11⋊C8—48no—
95C2×#125—24no—
96C2×#125—24no—
97C2×#125Dic1114yes—
98C2×#125C2×D1114yes—
99C22×C4⋊C4Dic1114yes—
100C22×C4⋊C4C2×D1112yes—
101C22×C42C2×D1111yescharacteristic
102#432—224no—
103#431—224no—
104#423—114no—
105#407—114no—
106C4×M16—114no—
107#343—1116no—
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×Dic1114yes—
121C23×C4C2×Dic1112yes—
122C23×C4C22×D1111yescharacteristic
123C2×M16—118no—
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×Dic11116yes—
136C2×C4⋊C4C2×Dic1114yes—
137C2×C4⋊C4C22×D1114yes—
138C2×C42C2×Dic1112yes—
139C2×C42C22⋊D1114yes—
140C2×C42C22⋊D1114yes—
141C2×C42C22×D1112yes—
142C4⋊C8—228no—
143C22⋊C8—228no—
144#97—224no—
145C4×C8—224no—
146C2×C11—22no—
147C2×C11—24no—
148C2×C11#231011yescharacteristic
149C2×C11C2×#41312yes—
150C24C22×Dic1111yescharacteristic
151C22×C4—24no—
152C22×C4—24no—
153C22×C4—24no—
154C22×C4—44no—
155C22×C4—48no—
156C22×C4C22⋊Dic1114yes—
157C22×C4C22⋊Dic1112yes—
158C22×C4C22⋊Dic1112yes—
159C22×C4C22×Dic1111yescharacteristic
160C22×C4C22×Dic1118yes—
161C22×C4C22×Dic1114yes—
162C22×C4C2×C22⋊D1114yes—
163C22×C4C23×D1111yescharacteristic
164M16—2216no—
165C2×C8—228no—
166C4⋊C4—28no—
167C4⋊C4—216no—
168C4⋊C4—216no—
169C4⋊C4—28no—
170C42C22⋊Dic1112yes—
171C42C22⋊Dic1114yes—
172C42C22⋊Dic1112yes—
173C42C2×C22⋊D1112yes—
174C42C2×C22⋊D1112yes—
175C42C2×C22⋊D1114yes—
176C11#2183011yescharacteristic, complemented, Sylow
177C23—22no—
178C23—24no—
179C23C2×C22⋊Dic1112yes—
180C23C23×Dic1111yescharacteristic
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×C22⋊Dic1112yes—
192C2×C4C2×C22⋊Dic1114yes—
193C2×C4C2×C22⋊Dic1114yes—
194C2×C4#6704014yes—
195C2×C4C22×C22⋊D1112yes—
196C8—448no—
197C22—28no—
198C22—22no—
199C22—22no—
200C22—22no—
201C22#1062285014yes—
202C22#1062334312yes—
203C22C22×C22⋊Dic1111yescharacteristic
204C4—22no—
205C4—24no—
206C4—24no—
207C4—48no—
208C4#1062334714yes—
209C2—22no—
210C2—24no—
211C2#1307120211yescharacteristic
212C2C2×#1062285012yes—
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#125C2
socleC22×C11C22×C22⋊C4
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenterC22×#125D11
hypocenterC11#21830
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C42 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
2. #13069610C2semidirect
176. C11#21830semidirect

Maximal subgroups

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

subgroupindex
#130772492
#130696102
#130686962
C22×C11×#1252
#2183011