Finite Group Databasebeta

← #16781049

Subgroups — #16781049

Order 3328.

810 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 810 conjugacy classes of subgroups — too many to draw. Only its 132 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#13130727C212yesmaximal
2C2×#11718285C214yesmaximal
3C22×#88144C211yesmaximal, characteristic
4C22×C13×C4⋊C4C411yescharacteristic
5C22×C4⋊Dic13C411yescharacteristic
6C22×C4⋊Dic13C2212yes—
7C22×#6101C412yes—
8C22×C4×Dic13C2211yescharacteristic
9C2×#88144—28no—
10C2×#88144—24no—
11C2×C22⋊#1057C2214yes—
12#11718290—24no—
13#11718285—28no—
14C23×C4×C13C2×C412yes—
15C23×C4×C13C2×C411yescharacteristic
16C23×Dic13C2×C411yescharacteristic
17C23×Dic13C2×C412yes—
18C23×Dic13C2311yescharacteristic
19C22×#1057—24no—
20C2×C13×C4⋊C4—24no—
21C2×C13×C4⋊C4—22no—
22C2×C4⋊Dic13—22no—
23C2×C4⋊Dic13—24no—
24C2×C4⋊Dic13—24no—
25C2×C4⋊Dic13—24no—
26C2×C4⋊Dic13D418yes—
27C2×#6101—24no—
28C2×#6101—24no—
29C2×#6101—24no—
30C2×C4×Dic13—24no—
31C2×C4×Dic13D414yes—
32#88144—232no—
33C22⋊#1057—28no—
34#8306—131nomaximal, Sylow
35C24×C13C22×C411yescharacteristic
36C22×C4×C13—22no—
37C22×C4×C13—24no—
38C22×C4×C13—22no—
39C22×C4×C13—22no—
40C22×C4×C13—28no—
41C22×C4×C13C22⋊C414yes—
42C22×C4×C13C22⋊C412yes—
43C22×Dic13—22no—
44C22×Dic13—22no—
45C22×Dic13—22no—
46C22×Dic13—24no—
47C22×Dic13—42no—
48C22×Dic13—44no—
49C22×Dic13C22⋊C412yes—
50C22×Dic13C22⋊C414yes—
51C22×Dic13C2×D412yes—
52C22×Dic13C2×D414yes—
53C2×#1057—48no—
54C2×#1057—44no—
55C13×C4⋊C4—28no—
56C4⋊Dic13—28no—
57C4⋊Dic13—216no—
58#6101—216no—
59C4×Dic13—28no—
60C22×#125—131no—
61#1817—132no—
62C2×#324—134no—
63C23×C13—22no—
64C23×C13—22no—
65C23×C13C2×C22⋊C412yes—
66C23×C13C2×C22⋊C411yescharacteristic
67C23×C13#13114yes—
68C2×C4×C13—28no—
69C2×C4×C13—22no—
70C2×C4×C13—22no—
71C2×C4×C13—24no—
72C2×C4×C13—28no—
73C2×C4×C13—44no—
74C2×C4×C13—44no—
75C2×C4×C13#10114yes—
76C2×Dic13—24no—
77C2×Dic13—22no—
78C2×Dic13—24no—
79C2×Dic13—24no—
80C2×Dic13—44no—
81C2×Dic13—44no—
82C2×Dic13—44no—
83C2×Dic13—44no—
84C2×Dic13—44no—
85C2×Dic13#12014yes—
86#1057—84no—
87C2×#125—264no—
88C2×#125—268no—
89C22×C4⋊C4—132no—
90C22×C4⋊C4—132no—
91C22×C4⋊C4—131no—
92C22×C4⋊C4#26111yescharacteristic
93C22×C42—131no—
94C2×C22⋊C8—134no—
95#336—264no—
96#324—268no—
97C22×C13—28no—
98C22×C13—22no—
99C22×C13—22no—
100C22×C13#37911yescharacteristic
101C22×C13#40814yes—
102C22×C13#40812yes—
103C22×C13#41012yes—
104C22×C13C2×#10112yes—
105C4×C13—24no—
106C4×C13—44no—
107Dic13—24no—
108Dic13—42no—
109Dic13—44no—
110C23×C4—131no—
111C23×C4—131no—
112C23×C4—132no—
113C23×C4C2×#26112yes—
114C23×C4C2×#26111yescharacteristic
115C22×C8—264no—
116#125—2632no—
117C2×C4⋊C4—24no—
118C2×C4⋊C4—22no—
119C2×C4⋊C4—138no—
120C2×C4⋊C4—264no—
121C2×C4⋊C4—264no—
122C2×C4⋊C4—264no—
123C2×C4⋊C4—264no—
124C2×C4⋊C4—264no—
125C2×C4⋊C4—264no—
126C2×C4⋊C4—262no—
127C2×C42—134no—
128C2×C42—264no—
129C22⋊C8—268no—
130C2×C13—24no—
131C2×C13#147014yes—
132C2×C13#178011yescharacteristic
133C2×C13#178211yescharacteristic
134C2×C13#178411yescharacteristic
135C24C22×#26111yescharacteristic
136C22×C4—22no—
137C22×C4—24no—
138C22×C4—28no—
139C22×C4—22no—
140C22×C4—22no—
141C22×C4—132no—
142C22×C4—134no—
143C22×C4—132no—
144C22×C4—134no—
145C22×C4—264no—
146C22×C4—262no—
147C22×C4—262no—
148C22×C4—262no—
149C22×C4—522no—
150C22×C4—524no—
151C22×C4C22⋊#26114yes—
152C22×C4C22⋊#26112yes—
153C2×C8—524no—
154C2×C8—528no—
155C4⋊C4—28no—
156C4⋊C4—2616no—
157C4⋊C4—2616no—
158C4⋊C4—268no—
159C42—268no—
160C13#830611yescharacteristic, complemented, Sylow
161C23—22no—
162C23—22no—
163C23#8823814yes—
164C23C2×C22⋊#26112yes—
165C23C2×C22⋊#26111yescharacteristic
166C2×C4—28no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—24no—
170C2×C4—28no—
171C2×C4—44no—
172C2×C4—44no—
173C2×C4—134no—
174C2×C4—264no—
175C2×C4—262no—
176C2×C4—264no—
177C2×C4—264no—
178C2×C4—524no—
179C2×C4—524no—
180C2×C4—524no—
181C2×C4—524no—
182C2×C4—524no—
183C2×C4#8811314yes—
184C8—1044no—
185C22—28no—
186C22—22no—
187C22—22no—
188C22C2×#8811312yes—
189C22#1171914614yes—
190C22#1171914712yes—
191C22#1171915612yes—
192C22#1171917111yescharacteristic
193C4—24no—
194C4—44no—
195C4—264no—
196C4—522no—
197C4—524no—
198C2—24no—
199C2#1313010914yes—
200C2#1313066011yescharacteristic
201C2#1313066711yescharacteristic
202C2#1313067011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutator, prime radicalC24×C13C22×C4
FrattiniC24C22×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
cosocleC23×Dic13C23
hypercenterC22×C4⋊C4#261
hypocenterC13#8306
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
160. C13#8306semidirect

Maximal subgroups

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

subgroupindex
#131307272
C2×#117182852
C22×#881442
#830613