Finite Group Databasebeta

← #13122903

Subgroups — #13122903

Order 1664.

380 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×C13×#125C211yesmaximal, characteristic
2C2×#88124C211yesmaximal, characteristic
3#11718647C212yesmaximal
4#11718645C214yesmaximal
5#11718644C212yesmaximal
6#11718643C212yesmaximal
7#11718641C212yesmaximal
8#11718597C211yesmaximal, characteristic
9C13×#125—24no—
10C2×C13×C4⋊C4C2211yescharacteristic
11C2×C13×C4⋊C4C2211yescharacteristic
12C2×C13×C4⋊C4C2212yes—
13C2×C13×C4⋊C4C2212yes—
14C2×C42×C13C2211yescharacteristic
15C2×C4⋊Dic13C2211yescharacteristic
16C2×C4⋊Dic13C2211yescharacteristic
17C2×C4⋊Dic13C2212yes—
18C2×#6101C2212yes—
19C2×#6101C2212yes—
20C2×#6101C2214yes—
21#88124—24no—
22#88071C2212yes—
23#88071C2212yes—
24#88071C2214yes—
25#88071C2214yes—
26#88071C2214yes—
27C22×C4×C13C2312yes—
28C22×C4×C13C2312yes—
29C22×C4×C13C2311yescharacteristic
30C22×C4×C13C2311yescharacteristic
31C22×C4×C13C2311yescharacteristic
32C22×Dic13C2314yes—
33C22×Dic13C2312yes—
34C22×Dic13C2312yes—
35C13×C4⋊C4—22no—
36C13×C4⋊C4—22no—
37C13×C4⋊C4—24no—
38C13×C4⋊C4—24no—
39C42×C13D414yes—
40C4⋊Dic13—22no—
41C4⋊Dic13—22no—
42C4⋊Dic13—42no—
43#6101—24no—
44#6101—24no—
45#6101—44no—
46#2822—131nomaximal, Sylow
47C23×C13C2411yescharacteristic
48C2×C4×C13—21no—
49C2×C4×C13—22no—
50C2×C4×C13—22no—
51C2×C4×C13—21no—
52C2×C4×C13—22no—
53C2×C4×C13—22no—
54C2×C4×C13—22no—
55C2×C4×C13—24no—
56C2×C4×C13—22no—
57C2×C4×C13C2×D412yes—
58C2×C4×C13C2×D412yes—
59C2×C4×C13C2×D412yes—
60C2×Dic13—22no—
61C2×Dic13—22no—
62C2×Dic13—22no—
63C2×Dic13—24no—
64C2×Dic13—24no—
65C2×Dic13—22no—
66C2×Dic13—24no—
67C2×Dic13—24no—
68C2×#125—131no—
69C2×#125D1311yescharacteristic
70#400—132no—
71#400—132no—
72#398—132no—
73#398—132no—
74#398—134no—
75#382—131no—
76C22×C13C22×D411yescharacteristic
77C22×C13H(5,𝔽2)11yescharacteristic
78C22×C132−1+412yes—
79C22×C132−1+412yes—
80C22×C132−1+411yescharacteristic
81C4×C13—22no—
82C4×C13—22no—
83C4×C13—22no—
84C4×C13—42no—
85C4×C13—42no—
86Dic13—42no—
87Dic13—42no—
88Dic13—44no—
89#125—24no—
90#125—264no—
91C2×C4⋊C4—132no—
92C2×C4⋊C4—132no—
93C2×C4⋊C4—131no—
94C2×C4⋊C4—131no—
95C2×C4⋊C4—134no—
96C2×C4⋊C4—132no—
97C2×C4⋊C4C2×D1312yes—
98C2×C4⋊C4C2×D1311yescharacteristic
99C2×C4⋊C4C2×D1312yes—
100C2×C4⋊C4C2×D1311yescharacteristic
101C2×C42C2×D1311yescharacteristic
102#95—132no—
103#95—132no—
104#95—134no—
105#95—134no—
106#95—134no—
107C2×C13#53611yescharacteristic
108C2×C13#53611yescharacteristic
109C2×C13#53711yescharacteristic
110C2×C13#56312yes—
111C2×C13#56412yes—
112C22×C4—134no—
113C22×C4—132no—
114C22×C4—132no—
115C22×C4C22×D1312yes—
116C22×C4C22×D1312yes—
117C22×C4C22×D1311yescharacteristic
118C22×C4C22×D1311yescharacteristic
119C22×C4C22×D1311yescharacteristic
120C4⋊C4—24no—
121C4⋊C4—22no—
122C4⋊C4—24no—
123C4⋊C4—22no—
124C4⋊C4—264no—
125C4⋊C4—264no—
126C4⋊C4—262no—
127C4⋊C4—262no—
128C4⋊C4—524no—
129C4⋊C4—522no—
130C42C22⋊D1314yes—
131C13#282211yescharacteristic, complemented, Sylow
132C23C23×D1311yescharacteristic
133C2×C4—22no—
134C2×C4—21no—
135C2×C4—22no—
136C2×C4—21no—
137C2×C4—22no—
138C2×C4—24no—
139C2×C4—22no—
140C2×C4—22no—
141C2×C4—22no—
142C2×C4—264no—
143C2×C4—264no—
144C2×C4—262no—
145C2×C4—264no—
146C2×C4—262no—
147C2×C4—264no—
148C2×C4—262no—
149C2×C4—262no—
150C2×C4C2×C22⋊D1312yes—
151C2×C4C2×C22⋊D1312yes—
152C2×C4C2×C22⋊D1312yes—
153C22#8825412yes—
154C22#8825611yescharacteristic
155C22#8825712yes—
156C22#8825711yescharacteristic
157C22C22×C22⋊D1311yescharacteristic
158C4—22no—
159C4—22no—
160C4—22no—
161C4—42no—
162C4—42no—
163C4—522no—
164C4—522no—
165C4—524no—
166C2C13⋊#56412yes—
167C2#1171940412yes—
168C2#1171952111yescharacteristic
169C2#1171953011yescharacteristic
170C2#1171953811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC2×C13×#125C2
hypercenterC2×#125D13
hypocenterC13#2822
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
131. C13#2822semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1252
C2×#881242
#117186472
#117186452
#117186442
#117186432
#117186412
#117185972
#282213