Finite Group Databasebeta

← #15756461

Subgroups — #15756461

Order 3328.

474 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 99 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#13113163C212yesmaximal
2#13112742C214yesmaximal, complemented
3C13×#2312C211yesmaximal, characteristic
4C22×C13×C22⋊C4C2211yescharacteristic
5C13×#388—24no—
6C13×#380C2212yes—
7C13×#379C412yes—
8C4×C13×C22⋊C4C412yes—
9#11718868C2214yes—
10#11718117—24no—
11C25×C13C2×C411yescharacteristic
12C23×C4×C13C2×C411yescharacteristic
13C23×C4×C13C2311yescharacteristic
14C2×C13×C4⋊C4—22no—
15C2×C13×C22⋊C4—24no—
16C2×C13×C22⋊C4—22no—
17C2×C13×C22⋊C4—22no—
18C2×C13×C22⋊C4C2×C414yes—
19C2×C13×C22⋊C4D414yes—
20C2×C42×C13—22no—
21C2×#6099—24no—
22C13×#95—22no—
23C13×#95—22no—
24C22⋊#1055—24no—
25C22⋊#1055—24no—
26#8759—131nomaximal, Sylow
27C24×C13—22no—
28C24×C13—42no—
29C24×C13—81no—
30C24×C13—81no—
31C24×C13C22⋊C412yes—
32C24×C13C22×C411yescharacteristic
33C22×C4×C13—22no—
34C22×C4×C13—24no—
35C22×C4×C13—81no—
36C22×C4×C13—81no—
37C22×C4×C13C22⋊C412yes—
38C22×C4×C13C2×D412yes—
39C22×C4×C13#4114yes—
40C13×C4⋊C4—82no—
41C13×C22⋊C4—28no—
42C13×C22⋊C4—44no—
43C13×C22⋊C4—82no—
44C13×C22⋊C4—82no—
45C42×C13—82no—
46#6099—84no—
47C2×#1055—44no—
48#2312D1311yescharacteristic
49#1462—132no—
50#1305—134no—
51C23×C13—22no—
52C23×C13—22no—
53C23×C13—24no—
54C23×C13—41no—
55C23×C13—41no—
56C23×C13—44no—
57C23×C13—42no—
58C23×C13—42no—
59C23×C13—82no—
60C23×C13—82no—
61C23×C13—88no—
62C23×C13C2×C22⋊C411yescharacteristic
63C23×C13#11712yes—
64C2×C4×C13—22no—
65C2×C4×C13—44no—
66C2×C4×C13—42no—
67C2×C4×C13—42no—
68C2×C4×C13—44no—
69C2×C4×C13—44no—
70C2×C4×C13—44no—
71C2×C4×C13—82no—
72C2×C4×C13#12314yes—
73#1055—84no—
74C22×C22⋊C4C2×D1311yescharacteristic
75#407—134no—
76#388—24no—
77#380C2×D1312yes—
78#379Dic1312yes—
79C4×C22⋊C4Dic1312yes—
80#323—264no—
81C22×C13—21no—
82C22×C13—21no—
83C22×C13—22no—
84C22×C13—22no—
85C22×C13—22no—
86C22×C13—44no—
87C22×C13—42no—
88C22×C13—42no—
89C22×C13—42no—
90C22×C13—84no—
91C22×C13—88no—
92C22×C13#38111yescharacteristic
93C22×C13#41312yes—
94C4×C13—24no—
95C4×C13—42no—
96C4×C13—84no—
97C25C2×Dic1311yescharacteristic
98C23×C4C2×Dic1311yescharacteristic
99C23×C4C22×D1311yescharacteristic
100C2×M16—264no—
101C2×C4⋊C4—22no—
102C2×C22⋊C4—24no—
103C2×C22⋊C4—22no—
104C2×C22⋊C4—22no—
105C2×C22⋊C4C2×Dic1314yes—
106C2×C22⋊C4C22⋊D1314yes—
107C2×C42—22no—
108C22⋊C8—264no—
109C22⋊C8—264no—
110#95—22no—
111#95—22no—
112C2×C13—22no—
113C2×C13—42no—
114C2×C13—82no—
115C2×C13#182211yescharacteristic
116C2×C13#182811yescharacteristic
117C2×C13#182911yescharacteristic
118C24—22no—
119C24—42no—
120C24—81no—
121C24—81no—
122C24C22⋊Dic1312yes—
123C24C22×Dic1311yescharacteristic
124C22×C4—22no—
125C22×C4—24no—
126C22×C4—81no—
127C22×C4—81no—
128C22×C4C22⋊Dic1312yes—
129C22×C4#612714yes—
130C22×C4C2×C22⋊D1312yes—
131M16—1044no—
132C2×C8—524no—
133C4⋊C4—82no—
134C22⋊C4—28no—
135C22⋊C4—44no—
136C22⋊C4—82no—
137C22⋊C4—82no—
138C42—82no—
139C13#875911yescharacteristic, complemented, Sylow
140C23—22no—
141C23—22no—
142C23—24no—
143C23—41no—
144C23—41no—
145C23—44no—
146C23—42no—
147C23—42no—
148C23—82no—
149C23—82no—
150C23—88no—
151C23#8818012yes—
152C23C2×C22⋊Dic1311yescharacteristic
153C2×C4—22no—
154C2×C4—42no—
155C2×C4—44no—
156C2×C4—42no—
157C2×C4—44no—
158C2×C4—44no—
159C2×C4—44no—
160C2×C4—82no—
161C2×C4#8818314yes—
162C8—1044no—
163C22—21no—
164C22—21no—
165C22—22no—
166C22—22no—
167C22—22no—
168C22—44no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22—84no—
173C22—88no—
174C22#1171887211yescharacteristic
175C22#1171889812yes—
176C4—24no—
177C4—42no—
178C4—84no—
179C2—22no—
180C2—42no—
181C2—82no—
182C2#1311491911yescharacteristic
183C2#1311494411yescharacteristic
184C2#1311494711yescharacteristic
subgroupG/H
centerC22#11718872
commutatorC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2312C2
socleC22×C13#381
prime radicalC25×C13C2×C4
cosocleC23×C4×C13C23
hypercenter#2312D13
hypocenterC13#8759
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2312

Complements

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

NH ≅ G/Ntype
2. #13112742C2semidirect
139. C13#8759semidirect

Maximal subgroups

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

subgroupindex
#131131632
#131127422
C13×#23122
#875913