Finite Group Databasebeta

← #15872372

Subgroups — #15872372

Order 3328.

1130 conjugacy classes of subgroups; only the 315 normal subgroups are shown.

normal subgroups only

This group has 1130 conjugacy classes of subgroups — too many to draw. Only its 315 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#13117434C212yesmaximal
2#13115822C218yesmaximal, complemented
3#13114910C214yesmaximal
4C2×C13×#543C211yesmaximal, characteristic
5C13×#543—28no—
6C2×C13×C22⋊Q8C418yescomplemented
7C2×C13×C22⋊Q8C2214yes—
8C22×C13×C22⋊C4C2212yes—
9C22×C13×C22⋊C4C2211yescharacteristic
10#11718908C2214yes—
11#11718873C2214yes—
12C4×C22⋊Dic13C2214yes—
13#11718612—28no—
14#11718118C22116yes—
15C25×C13C2311yescharacteristic
16C22×Q8×C13C2×C414yes—
17C23×C4×C13C2×C414yes—
18C23×C4×C13C2312yes—
19C13×C22⋊Q8—28no—
20C13×C22⋊Q8—28no—
21C13×C22⋊Q8—232no—
22C2×C13×C4⋊C4C2×C4112yes—
23C2×C13×C22⋊C4—28no—
24C2×C13×C22⋊C4C2×C414yes—
25C2×C13×C22⋊C4C2×C414yes—
26C2×C13×C22⋊C4D418yes—
27C2×C13×C22⋊C4C2314yes—
28C2×C22⋊Dic13—24no—
29C2×C22⋊Dic13—24no—
30C2×C22⋊Dic13C2318yes—
31C2×C4⋊Dic13—24no—
32C2×C4×Dic13—24no—
33#88071—24no—
34#88071—24no—
35#21827—131nomaximal, Sylow
36C24×C13—24no—
37C24×C13—82no—
38C24×C13C22×C412yes—
39C24×C13C2×D414yes—
40C24×C13C2411yescharacteristic
41C2×Q8×C13—28no—
42C2×Q8×C13—84no—
43C22×C4×C13—28no—
44C22×C4×C13—82no—
45C22×C4×C13—84no—
46C22×C4×C13C22×C418yes—
47C22×C4×C13C22×C414yes—
48C22×C4×C13C2×D414yes—
49C22×C4×C13C2×D414yes—
50C22×Dic13—28no—
51C13×C4⋊C4—224no—
52C13×C22⋊C4—28no—
53C13×C22⋊C4—28no—
54C13×C22⋊C4C22⋊C4116yes—
55C22⋊Dic13—216no—
56C22⋊Dic13—84no—
57C22⋊Dic13—84no—
58C4⋊Dic13—84no—
59C4×Dic13—84no—
60C2×#543D1311yescharacteristic
61#2312—132no—
62#1996—138no—
63#1819—134no—
64C23×C13—24no—
65C23×C13—28no—
66C23×C13—44no—
67C23×C13—42no—
68C23×C13—44no—
69C23×C13—44no—
70C23×C13—88no—
71C23×C13C2×C22⋊C414yes—
72C23×C13C23×C411yescharacteristic
73C23×C13C22×D412yes—
74C23×C132−1+414yes—
75Q8×C13—88no—
76C2×C4×C13—28no—
77C2×C4×C13—44no—
78C2×C4×C13—44no—
79C2×C4×C13—44no—
80C2×C4×C13—48no—
81C2×C4×C13—88no—
82C2×C4×C13C2×C22⋊C418yes—
83C2×Dic13—48no—
84C2×Dic13—48no—
85C2×Dic13—48no—
86#543—28no—
87C2×C22⋊Q8Dic1318yescomplemented
88C2×C22⋊Q8C2×D1314yes—
89C22×C22⋊C4C2×D1312yes—
90C22×C22⋊C4C2×D1311yescharacteristic
91#388—268no—
92#380—134no—
93#379—134no—
94C4×C22⋊C4—134no—
95#342—1316no—
96C22×C13—22no—
97C22×C13—22no—
98C22×C13—22no—
99C22×C13—24no—
100C22×C13—28no—
101C22×C13—44no—
102C22×C13—48no—
103C22×C13—88no—
104C22×C13C22×C22⋊C411yescharacteristic
105C22×C13#51912yes—
106C22×C13#53614yes—
107C4×C13—28no—
108C4×C13—48no—
109Dic13—88no—
110C25C22×D1311yescharacteristic
111C22×Q8C2×Dic1314yes—
112C23×C4C2×Dic1314yes—
113C23×C4C22×D1312yes—
114C22⋊Q8—28no—
115C22⋊Q8—28no—
116C22⋊Q8—232no—
117C2×C4⋊C4—264no—
118C2×C4⋊C4C2×Dic13112yes—
119C2×C22⋊C4—28no—
120C2×C22⋊C4—138no—
121C2×C22⋊C4—264no—
122C2×C22⋊C4—264no—
123C2×C22⋊C4C2×Dic1314yes—
124C2×C22⋊C4C2×Dic1314yes—
125C2×C22⋊C4C22⋊D1318yes—
126C2×C22⋊C4C22×D1314yes—
127C2×C42—264no—
128#95—264no—
129#95—264no—
130C2×C13—24no—
131C2×C13—22no—
132C2×C13—44no—
133C2×C13#231011yescharacteristic
134C2×C13#288312yes—
135C24—24no—
136C24—82no—
137C24C22×Dic1312yes—
138C24C2×C22⋊D1314yes—
139C24C23×D1311yescharacteristic
140C2×Q8—28no—
141C2×Q8—84no—
142C22×C4—28no—
143C22×C4—82no—
144C22×C4—84no—
145C22×C4—268no—
146C22×C4C22×Dic1318yes—
147C22×C4C22×Dic1314yes—
148C22×C4C2×C22⋊D1314yes—
149C22×C4C2×C22⋊D1314yes—
150C4⋊C4—224no—
151C4⋊C4—1044no—
152C22⋊C4—28no—
153C22⋊C4—28no—
154C22⋊C4—2616no—
155C22⋊C4—1044no—
156C22⋊C4—1044no—
157C22⋊C4C22⋊Dic13116yes—
158C42—1044no—
159C13#2182711yescharacteristic, complemented, Sylow
160C23—24no—
161C23—28no—
162C23—44no—
163C23—42no—
164C23—44no—
165C23—44no—
166C23—88no—
167C23C2×C22⋊Dic1314yes—
168C23#8825414yes—
169C23C23×Dic1311yescharacteristic
170C23C22×C22⋊D1312yes—
171Q8—88no—
172C2×C4—28no—
173C2×C4—44no—
174C2×C4—44no—
175C2×C4—44no—
176C2×C4—48no—
177C2×C4—88no—
178C2×C4—528no—
179C2×C4—528no—
180C2×C4—528no—
181C2×C4C2×C22⋊Dic1318yes—
182C22—22no—
183C22—22no—
184C22—22no—
185C22—28no—
186C22—24no—
187C22—44no—
188C22—48no—
189C22—88no—
190C22#1171951712yes—
191C22#1171952114yes—
192C22C22×C22⋊Dic1311yescharacteristic
193C4—28no—
194C4—48no—
195C4—1048no—
196C2—24no—
197C2—22no—
198C2—44no—
199C2#1311742211yescharacteristic
200C2#1312329712yes—
subgroupG/H
centerC22C22×C22⋊Dic13
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC2×C13×#543C2
socleC22×C13C22×C22⋊C4
prime radicalC25×C13C23
cosocleC24×C13C24
hypercenterC2×#543D13
hypocenterC13#21827
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C22⋊C4 ◁ C2×#543

Complements

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

NH ≅ G/Ntype
2. #13115822C2semidirect
6. C2×C13×C22⋊Q8C4semidirect
87. C2×C22⋊Q8Dic13semidirect
159. C13#21827semidirect

Maximal subgroups

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

subgroupindex
#131174342
#131158222
#131149102
C2×C13×#5432
#2182713