Finite Group Databasebeta

← #14647108

Subgroups — #14647108

Order 2816.

786 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 786 conjugacy classes of subgroups — too many to draw. Only its 139 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#13068526C212yesmaximal
2#13066459C214yesmaximal, complemented
3C2×C11×#381C211yesmaximal, characteristic
4C24×C4×C11C2211yescharacteristic
5C22×C11×C22⋊C4C412yes—
6C11×#381—24no—
7C2×C11×#95C412yes—
8C2×C11×#95C2212yes—
9C2×C22⋊(C11⋊C8)—24no—
10C2×C22⋊(C11⋊C8)C2214yes—
11C25×C11C2×C411yescharacteristic
12C23×C4×C11—24no—
13C23×C4×C11—44no—
14C23×C4×C11C2×C414yes—
15C23×C4×C11C2×C411yescharacteristic
16C23×C4×C11D414yes—
17C23×C4×C11C2311yescharacteristic
18C2×C11×C22⋊C4—22no—
19C2×C11×C22⋊C4—22no—
20C2×C11×C22⋊C4—44no—
21C22×C11⋊C8—24no—
22C11×#95—24no—
23C11×#95—24no—
24C22⋊(C11⋊C8)—28no—
25C22⋊(C11⋊C8)—48no—
26#8702—111nomaximal, Sylow
27C24×C11—24no—
28C24×C11—22no—
29C24×C11—24no—
30C24×C11—42no—
31C24×C11C22⋊C412yes—
32C24×C11C22×C411yescharacteristic
33C22×C4×C11—28no—
34C22×C4×C11—22no—
35C22×C4×C11—28no—
36C22×C4×C11—24no—
37C22×C4×C11—28no—
38C22×C4×C11—42no—
39C22×C4×C11—44no—
40C22×C4×C11—42no—
41C22×C4×C11—416no—
42C22×C4×C11—44no—
43C22×C4×C11—44no—
44C22×C4×C11C22⋊C412yes—
45C22×C4×C11C2×D412yes—
46C22×C4×C11#4114yes—
47C11×C22⋊C4—44no—
48C11×C22⋊C4—44no—
49C2×C11⋊C8—48no—
50C2×C11⋊C8—44no—
51C2×#381D1111yescharacteristic
52#1779—112no—
53#1280—114no—
54C23×C11—22no—
55C23×C11—22no—
56C23×C11—28no—
57C23×C11—22no—
58C23×C11—24no—
59C23×C11—22no—
60C23×C11—24no—
61C23×C11—416no—
62C23×C11—44no—
63C23×C11—44no—
64C23×C11#9914yes—
65C23×C11C2×C22⋊C411yescharacteristic
66C23×C11#11712yes—
67C23×C11#13114yes—
68C2×C4×C11—24no—
69C2×C4×C11—22no—
70C2×C4×C11—24no—
71C2×C4×C11—44no—
72C2×C4×C11—416no—
73C2×C4×C11—44no—
74C2×C4×C11—44no—
75C2×C4×C11—44no—
76C2×C4×C11—44no—
77C2×C4×C11—88no—
78C2×C4×C11#12314yes—
79C11⋊C8—84no—
80C24×C4C2×D1111yescharacteristic
81C22×C22⋊C4Dic1112yes—
82C2×C22⋊C8—114no—
83C2×C22⋊C8—224no—
84#381—24no—
85C2×#95Dic1112yes—
86C2×#95C2×D1112yes—
87C22×C11—22no—
88C22×C11—22no—
89C22×C11—28no—
90C22×C11—24no—
91C22×C11—28no—
92C22×C11—416no—
93C22×C11—42no—
94C22×C11—42no—
95C22×C11—44no—
96C22×C11#38111yescharacteristic
97C22×C11#40812yes—
98C22×C11C2×#9912yes—
99C22×C11#41312yes—
100C22×C11#43314yes—
101C4×C11—24no—
102C4×C11—42no—
103C4×C11—84no—
104C25C2×Dic1111yescharacteristic
105C23×C4—24no—
106C23×C4—44no—
107C23×C4C2×Dic1114yes—
108C23×C4C2×Dic1111yescharacteristic
109C23×C4C22⋊D1114yes—
110C23×C4C22×D1111yescharacteristic
111C22×C8—224no—
112C2×C22⋊C4—22no—
113C2×C22⋊C4—22no—
114C2×C22⋊C4—44no—
115C22⋊C8—228no—
116C22⋊C8—448no—
117#95—24no—
118#95—24no—
119C2×C11—24no—
120C2×C11—44no—
121C2×C11#146814yes—
122C2×C11#181811yescharacteristic
123C2×C11#181911yescharacteristic
124C2×C11#182211yescharacteristic
125C24—24no—
126C24—22no—
127C24—24no—
128C24—42no—
129C24C22⋊Dic1112yes—
130C24C22×Dic1111yescharacteristic
131C22×C4—28no—
132C22×C4—22no—
133C22×C4—28no—
134C22×C4—24no—
135C22×C4—28no—
136C22×C4—42no—
137C22×C4—42no—
138C22×C4—44no—
139C22×C4—416no—
140C22×C4—44no—
141C22×C4—44no—
142C22×C4C22⋊Dic1112yes—
143C22×C4#433914yes—
144C22×C4C2×C22⋊D1112yes—
145C2×C8—448no—
146C2×C8—444no—
147C22⋊C4—44no—
148C22⋊C4—44no—
149C11#870211yescharacteristic, complemented, Sylow
150C23—22no—
151C23—22no—
152C23—28no—
153C23—22no—
154C23—22no—
155C23—24no—
156C23—24no—
157C23—416no—
158C23—44no—
159C23—44no—
160C23#6689814yes—
161C23#6697912yes—
162C23#6700114yes—
163C23C2×C22⋊Dic1111yescharacteristic
164C2×C4—24no—
165C2×C4—22no—
166C2×C4—24no—
167C2×C4—44no—
168C2×C4—416no—
169C2×C4—44no—
170C2×C4—44no—
171C2×C4—44no—
172C2×C4—44no—
173C2×C4—88no—
174C2×C4#6698214yes—
175C8—884no—
176C22—22no—
177C22—22no—
178C22—28no—
179C22—24no—
180C22—28no—
181C22—416no—
182C22—42no—
183C22—42no—
184C22—44no—
185C22#1062261314yes—
186C22#1062282411yescharacteristic
187C22C2×#6689812yes—
188C22#1062284712yes—
189C22#1062285012yes—
190C4—24no—
191C4—42no—
192C4—84no—
193C2—24no—
194C2—44no—
195C2#1306696414yes—
196C2#1306868711yescharacteristic
197C2#1306869011yescharacteristic
198C2#1306869911yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#381C2
socleC23×C11C2×C22⋊C4
prime radicalC25×C11C2×C4
cosocleC23×C4×C11C23
hypercenterC2×#381D11
hypocenterC11#8702
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
2. #13066459C2semidirect
149. C11#8702semidirect

Maximal subgroups

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

subgroupindex
#130685262
#130664592
C2×C11×#3812
#870211