Finite Group Databasebeta

← #13119303

Subgroups — #13119303

Order 1664.

708 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C22×C13×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#88184C211yesmaximal, characteristic
3C2×#88183C214yesmaximal, complemented
4C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
5#11718653C214yesmaximal, complemented
6#11718649C212yesmaximal, complemented
7#11718637C212yesmaximal, complemented
8C23×C4×C13C2212yes—
9C23×C4×C13C2211yescharacteristic
10C22×C22⋊D13C2212yes—
11C22×D52C2211yescharacteristic
12C2×C13×C4⋊C4—24no—
13C2×C13×C4⋊C4C2212yes—
14C2×C13×C4⋊C4C2212yes—
15C2×C22⋊Dic13C2212yes—
16#88184—24no—
17#88183—216no—
18C2×#6103C2218yes—
19C2×#6103C2212yes—
20C2×C4⋊Dic13C2211yescharacteristic
21C2×#6101C2218yes—
22C2×C4×Dic13C2212yes—
23#88071C2212yes—
24C24×C13C2311yescharacteristic
25C23×D13C2312yes—
26C22×C4×C13—24no—
27C22×C4×C13—28no—
28C22×C4×C13—24no—
29C22×C4×C13D414yes—
30C22×C4×C13C2314yes—
31C22×C4×C13C2311yescharacteristic
32C22×C4×C13C2311yescharacteristic
33C2×C22⋊D13—28no—
34C2×C22⋊D13—24no—
35C22×Dic13C2312yes—
36C22×Dic13C2314yes—
37C2×D52—22no—
38C2×D52—24no—
39C13×C4⋊C4—24no—
40C13×C4⋊C4—24no—
41C22⋊Dic13D418yescomplemented
42#6103—24no—
43#6103—216no—
44C4⋊Dic13—22no—
45#6101—216no—
46C4×Dic13—24no—
47#2501—131nomaximal, Sylow
48C23×C13—22no—
49C23×C13—22no—
50C23×C13C2×D414yes—
51C23×C13C2×D412yes—
52C23×C13C2411yescharacteristic
53C22×D13—24no—
54C22×D13—22no—
55C22×D13—24no—
56C22×D13—24no—
57C2×C4×C13—22no—
58C2×C4×C13—28no—
59C2×C4×C13—28no—
60C2×C4×C13—24no—
61C2×C4×C13—48no—
62C2×C4×C13C2×D412yes—
63C2×C4×C13C2×D412yes—
64C2×C4×C13#4114yes—
65C22⋊D13—48no—
66C2×Dic13—24no—
67C2×Dic13—24no—
68C2×Dic13—24no—
69C2×Dic13—22no—
70C2×Dic13C2×D418yes—
71D52—44no—
72C2×#123—134no—
73C2×#121—131no—
74C22×C4⋊C4D1311yescharacteristic, complemented
75#399—134no—
76#390—132no—
77#384—132no—
78C4×C22⋊C4—131no—
79C22×C13—22no—
80C22×C13—22no—
81C22×C13—28no—
82C22×C13#12714yes—
83C22×C13C22×D412yes—
84C22×C13C22×D411yescharacteristic
85C22×C13C2×#4112yes—
86C22×C132−1+412yes—
87C2×D13—42no—
88C2×D13—42no—
89C2×D13—42no—
90C2×D13—48no—
91C4×C13—22no—
92C4×C13—44no—
93C4×C13#12314yescomplemented
94Dic13—28no—
95Dic13—42no—
96C22×D4—132no—
97C22×D4—131no—
98C23×C4C2×D1312yes—
99C23×C4C2×D1311yescharacteristic
100#123—2616no—
101#121—264no—
102C2×C4⋊C4—24no—
103C2×C4⋊C4—131no—
104C2×C4⋊C4—138no—
105C2×C4⋊C4C2×D1312yes—
106C2×C4⋊C4C2×D1312yes—
107C2×C22⋊C4—132no—
108C2×C22⋊C4—132no—
109C2×C22⋊C4—138no—
110C2×C42—132no—
111#95—132no—
112C2×C13—24no—
113C2×C13C2×#12311yescharacteristic
114C2×C13C2×#12711yescharacteristic
115C2×C13#53611yescharacteristic
116C2×C13#54714yes—
117D13—82no—
118C24—132no—
119C24C22×D1311yescharacteristic
120C2×D4—268no—
121C2×D4—264no—
122C2×D4—264no—
123C2×D4—262no—
124C22×C4—24no—
125C22×C4—28no—
126C22×C4—24no—
127C22×C4—134no—
128C22×C4—132no—
129C22×C4C22⋊D1314yes—
130C22×C4C22×D1314yes—
131C22×C4C22×D1311yescharacteristic
132C22×C4C22×D1311yescharacteristic
133C4⋊C4—24no—
134C4⋊C4—24no—
135C4⋊C4—2616no—
136C4⋊C4—262no—
137C22⋊C4—138no—
138C22⋊C4—2616no—
139C22⋊C4—264no—
140C42—264no—
141C13#250111yescharacteristic, complemented, Sylow
142C23—22no—
143C23—22no—
144C23—264no—
145C23—264no—
146C23—264no—
147C23—262no—
148C23D4×D1314yes—
149C23C2×C22⋊D1312yes—
150C23C23×D1311yescharacteristic
151D4—528no—
152D4—524no—
153C2×C4—22no—
154C2×C4—28no—
155C2×C4—28no—
156C2×C4—24no—
157C2×C4—48no—
158C2×C4—138no—
159C2×C4—264no—
160C2×C4—264no—
161C2×C4—264no—
162C2×C4—262no—
163C2×C4#612714yes—
164C2×C4C2×C22⋊D1312yes—
165C2×C4C2×C22⋊D1312yes—
166C22—28no—
167C22—22no—
168C22—22no—
169C22—528no—
170C22—522no—
171C22—522no—
172C22—522no—
173C22#8819414yes—
174C22C2×#612712yes—
175C22C2×D4×D1312yes—
176C22#8825412yes—
177C22C22×C22⋊D1311yescharacteristic
178C4—22no—
179C4—44no—
180C4—268no—
181C4—522no—
182C4#8818314yescomplemented
183C2—24no—
184C2—1042no—
185C2#1171921214yes—
186C2C2×#8818311yescharacteristic
187C2C2×#8819411yescharacteristic
188C2#1171952111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC22×C13×C4⋊C4C2
prime radicalC2×#88184C2
hypercenterC22×C4⋊C4D13
hypocenterC13#2501
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C13×C4⋊C4C2semidirect
3. C2×#88183C2semidirect
4. C4×C22⋊Dic13C2semidirect
5. #11718653C2semidirect
6. #11718649C2semidirect
7. #11718637C2semidirect
41. C22⋊Dic13D4semidirect
74. C22×C4⋊C4D13semidirect
93. C4×C13#123semidirect
141. C13#2501semidirect
182. C4#88183semidirect

Maximal subgroups

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

subgroupindex
C22×C13×C4⋊C42
C2×#881842
C2×#881832
C4×C22⋊Dic132
#117186532
#117186492
#117186372
#250113