Finite Group Databasebeta

← #16782264

Subgroups — #16782264

Order 3328.

566 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 76 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#13130670C212yesmaximal
2#13129739C214yesmaximal
3#13117421C211yesmaximal, characteristic
4C23×Dic26C2211yescharacteristic
5C2×#88131C412yes—
6#11719169C2214yes—
7C2×#88113—24no—
8C13×#381C411yescharacteristic
9#11718872C411yescharacteristic
10#11718604C2212yes—
11#11718307—24no—
12C23×C4×C13C2×C411yescharacteristic
13C23×Dic13C2×C411yescharacteristic
14C23×Dic13C2311yescharacteristic
15C22×Dic26—24no—
16C22×Dic26—44no—
17C22×Dic26D414yes—
18C2×#6122—24no—
19C2×C13×C22⋊C4C2×C412yes—
20C2×C22⋊Dic13C2×C412yes—
21C2×#6101—22no—
22C2×C4×Dic13—22no—
23#88131—44no—
24C22⋊#1057—28no—
25#88113—48no—
26C13×#95—22no—
27#88071—22no—
28#88071—24no—
29#8753—131nomaximal, Sylow
30C24×C13C22×C411yescharacteristic
31C22×C4×C13—22no—
32C22×C4×C13—22no—
33C22×C4×C13—42no—
34C22×C4×C13C22⋊C412yes—
35C22×Dic13—22no—
36C22×Dic13—24no—
37C22×Dic13—22no—
38C22×Dic13—42no—
39C22×Dic13C22⋊C412yes—
40C22×Dic13C2×D412yes—
41C22×Dic13#4114yes—
42C2×Dic26—28no—
43C2×Dic26—28no—
44C2×Dic26—44no—
45C2×Dic26—416no—
46#6122—48no—
47C2×#1057—44no—
48C13×C22⋊C4—42no—
49C22⋊Dic13—42no—
50#6101—44no—
51C4×Dic13—44no—
52#2310—131no—
53#1784—132no—
54#1306—134no—
55C23×C13—22no—
56C23×C13—42no—
57C23×C13C2×C22⋊C411yescharacteristic
58C23×C13#11712yes—
59C2×C4×C13—22no—
60C2×C4×C13—24no—
61C2×C4×C13—44no—
62C2×C4×C13—44no—
63C2×C4×C13—42no—
64C2×Dic13—28no—
65C2×Dic13—22no—
66C2×Dic13—22no—
67C2×Dic13—24no—
68C2×Dic13—44no—
69C2×Dic13—44no—
70C2×Dic13—42no—
71C2×Dic13#9914yes—
72C2×Dic13#12314yes—
73Dic26—416no—
74#1057—84no—
75C23×Q8—131no—
76C2×#117—132no—
77C2×#101—264no—
78#407—134no—
79#391—264no—
80#381—131no—
81#381—132no—
82#381#26111yescharacteristic
83C22×C13—22no—
84C22×C13—22no—
85C22×C13—24no—
86C22×C13—44no—
87C22×C13#38111yescharacteristic
88C22×C13C2×#9912yes—
89C4×C13—42no—
90C4×C13—82no—
91Dic13—24no—
92Dic13—24no—
93Dic13—82no—
94C22×Q8—134no—
95C22×Q8—264no—
96C22×Q8—524no—
97C23×C4—131no—
98C23×C4—131no—
99C23×C4C2×#26111yescharacteristic
100C2×M16—264no—
101#117—524no—
102C2×C4⋊C4—262no—
103C2×C22⋊C4—132no—
104C2×C22⋊C4C2×#26112yes—
105C2×C42—262no—
106#101—528no—
107C22⋊C8—268no—
108#95—22no—
109#95—264no—
110#95—262no—
111C2×C13—22no—
112C2×C13—42no—
113C2×C13#181911yescharacteristic
114C2×C13#183012yes—
115C24C22×#26111yescharacteristic
116C2×Q8—268no—
117C2×Q8—268no—
118C2×Q8—524no—
119C2×Q8—5216no—
120C22×C4—22no—
121C22×C4—22no—
122C22×C4—42no—
123C22×C4—132no—
124C22×C4—132no—
125C22×C4—134no—
126C22×C4—264no—
127C22×C4—262no—
128C22×C4—262no—
129C22×C4—522no—
130C22×C4C22⋊#26112yes—
131M16—528no—
132C2×C8—524no—
133C4⋊C4—524no—
134C22⋊C4—42no—
135C22⋊C4—522no—
136C42—524no—
137C13#875311yescharacteristic, complemented, Sylow
138C23—22no—
139C23—42no—
140C23#8823712yes—
141C23C2×C22⋊#26111yescharacteristic
142Q8—5216no—
143C2×C4—22no—
144C2×C4—24no—
145C2×C4—44no—
146C2×C4—44no—
147C2×C4—42no—
148C2×C4—134no—
149C2×C4—134no—
150C2×C4—268no—
151C2×C4—262no—
152C2×C4—262no—
153C2×C4—264no—
154C2×C4—524no—
155C2×C4—524no—
156C2×C4—522no—
157C8—1044no—
158C22—22no—
159C22—22no—
160C22—24no—
161C22—44no—
162C22#1171913511yescharacteristic
163C22D13⋊#9912yes—
164C4—42no—
165C4—82no—
166C4—264no—
167C4—264no—
168C4—1042no—
169C2—22no—
170C2—42no—
171C2#1313073211yescharacteristic
172C2#1313075012yes—
subgroupG/H
centerC22#11719135
commutator, prime radicalC24×C13C22×C4
FrattiniC24C22×#261
FittingC13×#381C4
socleC22×C13#381
cosocleC23×Dic13C23
hypercenter#381#261
hypocenterC13#8753
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
137. C13#8753semidirect

Maximal subgroups

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

subgroupindex
#131306702
#131297392
#131174212
#875313