Finite Group Databasebeta

← #13120713

Subgroups — #13120713

Order 1664.

416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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×C4×Dic26C211yesmaximal, characteristic
3#11718647C212yesmaximal
4#11718643C212yesmaximal
5#11718641C212yesmaximal
6#11718640C212yesmaximal
7#11718639C214yesmaximal
8#11718598C211yesmaximal, characteristic
9C22×Dic26C2211yescharacteristic
10C13×#125—24no—
11C2×C13×C4⋊C4C2212yes—
12C2×C13×C4⋊C4C2212yes—
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C42×C13C2211yescharacteristic
16C2×C4⋊Dic13C2211yescharacteristic
17C2×#6101C2212yes—
18C2×#6101C2214yes—
19C2×C4×Dic13C2212yes—
20C4×Dic26—24no—
21#88071C2212yes—
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—
35C2×Dic26—22no—
36C2×Dic26—24no—
37C13×C4⋊C4—24no—
38C13×C4⋊C4—22no—
39C13×C4⋊C4—22no—
40C13×C4⋊C4—24no—
41C42×C13D414yes—
42C4⋊Dic13—22no—
43#6101—24no—
44#6101—28no—
45C4×Dic13—24no—
46#2634—131nomaximal, Sylow
47C23×C13C2411yescharacteristic
48C2×C4×C13—22no—
49C2×C4×C13—22no—
50C2×C4×C13—22no—
51C2×C4×C13—22no—
52C2×C4×C13—22no—
53C2×C4×C13—24no—
54C2×C4×C13—24no—
55C2×C4×C13C2×D412yes—
56C2×C4×C13C2×D412yes—
57C2×C4×C13C2×D412yes—
58C2×Dic13—22no—
59C2×Dic13—22no—
60C2×Dic13—22no—
61C2×Dic13—24no—
62C2×Dic13—24no—
63C2×Dic13—24no—
64C2×Dic13—24no—
65C2×Dic13#4114yes—
66Dic26—28no—
67C2×#125D1311yescharacteristic
68C2×C4×Q8—131no—
69#400—132no—
70#400—132no—
71#398—132no—
72#395—132no—
73#387—134no—
74#383—131no—
75C22×C13C22×D411yescharacteristic
76C22×C13C2×#4112yes—
77C22×C132−1+412yes—
78C22×C132−1+412yes—
79C4×C13—22no—
80C4×C13—22no—
81C4×C13—22no—
82C4×C13—42no—
83C4×C13—42no—
84Dic13—24no—
85Dic13—42no—
86Dic13—44no—
87C22×Q8—131no—
88#125—24no—
89C4×Q8—264no—
90C2×C4⋊C4—132no—
91C2×C4⋊C4—131no—
92C2×C4⋊C4—134no—
93C2×C4⋊C4C2×D1312yes—
94C2×C4⋊C4C2×D1312yes—
95C2×C4⋊C4C2×D1311yescharacteristic
96C2×C4⋊C4C2×D1311yescharacteristic
97C2×C42—132no—
98C2×C42C2×D1311yescharacteristic
99#95—132no—
100#95—132no—
101#95—132no—
102#95—134no—
103#95—134no—
104#95—134no—
105C2×C13#52511yescharacteristic
106C2×C13#53611yescharacteristic
107C2×C13#53611yescharacteristic
108C2×C13#54114yes—
109C2×Q8—264no—
110C2×Q8—262no—
111C22×C4—132no—
112C22×C4—134no—
113C22×C4—132no—
114C22×C4C22×D1312yes—
115C22×C4C22×D1312yes—
116C22×C4C22×D1311yescharacteristic
117C22×C4C22×D1311yescharacteristic
118C22×C4C22×D1311yescharacteristic
119C4⋊C4—24no—
120C4⋊C4—22no—
121C4⋊C4—22no—
122C4⋊C4—24no—
123C4⋊C4—268no—
124C4⋊C4—264no—
125C4⋊C4—262no—
126C42—264no—
127C42C22⋊D1314yes—
128C13#263411yescharacteristic, complemented, Sylow
129C23C23×D1311yescharacteristic
130Q8—268no—
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—24no—
135C2×C4—24no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—134no—
139C2×C4—262no—
140C2×C4—262no—
141C2×C4—264no—
142C2×C4—264no—
143C2×C4—264no—
144C2×C4—264no—
145C2×C4—262no—
146C2×C4C2×C22⋊D1312yes—
147C2×C4C2×C22⋊D1312yes—
148C2×C4C2×C22⋊D1312yes—
149C22#8825412yes—
150C22#41×D1312yes—
151C22#8825712yes—
152C22C22×C22⋊D1311yescharacteristic
153C4—22no—
154C4—22no—
155C4—22no—
156C4—42no—
157C4—42no—
158C4—264no—
159C4—522no—
160C4—524no—
161C2#1171940114yes—
162C2#1171952111yescharacteristic
163C2#1171953011yescharacteristic
164C2#1171953311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC2×C13×#125C2
hypercenterC2×#125D13
hypocenterC13#2634
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
128. C13#2634semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1252
C2×C4×Dic262
#117186472
#117186432
#117186412
#117186402
#117186392
#117185982
#263413