Finite Group Databasebeta

← #13114444

Subgroups — #13114444

Order 1664.

168 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C13×#487C211yesmaximal, characteristic
2#11718754C211yesmaximal, characteristic
3#11718742C211yesmaximal, characteristic
4#11718739C211yesmaximal, characteristic
5#11718739C211yesmaximal, characteristic
6#11718342C211yesmaximal, characteristic
7C8×#1055C211yesmaximal, characteristic
8C13×C4⋊Q8C2211yescharacteristic
9C13×C4⋊Q8C2211yescharacteristic
10#88123C2211yescharacteristic
11#88123C2211yescharacteristic
12C13×#103—22no—
13C4×C8×C13C2211yescharacteristic
14#88075—22no—
15#88056—22no—
16#88050—22no—
17#88047—22no—
18#88047—22no—
19C4×#1055C2211yescharacteristic
20C4×#1055C2211yescharacteristic
21C2×Q8×C13—21no—
22C2×Q8×C13—21no—
23C2×Dic26—21no—
24C2×Dic26—21no—
25C2×C8×C13D412yes—
26C13×C4⋊C4—21no—
27C13×C4⋊C4—21no—
28C13×C4⋊C4—21no—
29C13×C4⋊C4—21no—
30C42×C13C2311yescharacteristic
31C4⋊Dic13—21no—
32C4⋊Dic13—21no—
33C4⋊Dic13—21no—
34C4⋊Dic13—21no—
35C2×#1055D412yes—
36C2×#1055D412yes—
37#1710—131nomaximal, Sylow
38Q8×C13—42no—
39Q8×C13—42no—
40C2×C4×C13—41no—
41C2×C4×C13—41no—
42C2×C4×C13C2×D411yescharacteristic
43C2×C4×C13C2×D411yescharacteristic
44C2×C4×C13C2×D411yescharacteristic
45C2×Dic13—41no—
46C2×Dic13—41no—
47Dic26—42no—
48Dic26—42no—
49C8×C13—22no—
50#1055—22no—
51#1055Q1614yes—
52#500—131no—
53#500—131no—
54#487—131no—
55#487—131no—
56#487—131no—
57#487D1311yescharacteristic
58C82—131no—
59C22×C13#12711yescharacteristic
60C4×C13—81no—
61C4×C13—81no—
62C4×C13C2×Q1612yes—
63C4×C13#13512yes—
64C4×C13#13512yes—
65Dic13—81no—
66Dic13—81no—
67C4⋊Q8—131no—
68C4⋊Q8—131no—
69C4⋊Q8C2×D1311yescharacteristic
70C4⋊Q8C2×D1311yescharacteristic
71#107—262no—
72#107—262no—
73#103—22no—
74#103—262no—
75#103—262no—
76#103—262no—
77C4×C8—131no—
78C4×C8—131no—
79C4×C8C2×D1311yescharacteristic
80C2×C13#49411yescharacteristic
81C2×C13#49511yescharacteristic
82C2×C13#49511yescharacteristic
83C2×Q8—21no—
84C2×Q8—21no—
85C2×Q8—261no—
86C2×Q8—261no—
87C2×C8—132no—
88C2×C8—132no—
89C2×C8C22⋊D1312yes—
90C4⋊C4—21no—
91C4⋊C4—21no—
92C4⋊C4—21no—
93C4⋊C4—21no—
94C4⋊C4—261no—
95C4⋊C4—261no—
96C4⋊C4—261no—
97C4⋊C4—261no—
98C42C22×D1311yescharacteristic
99C13#171011yescharacteristic, complemented, Sylow
100Q8—42no—
101Q8—42no—
102Q8—522no—
103Q8—522no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—521no—
107C2×C4—521no—
108C2×C4D4×D1311yescharacteristic
109C2×C4D4×D1311yescharacteristic
110C2×C4C2×C22⋊D1311yescharacteristic
111C8—22no—
112C8—134no—
113C8—262no—
114C22#8819411yescharacteristic
115C4—81no—
116C4—81no—
117C4—1041no—
118C4—1041no—
119C4#8817012yes—
120C4Q16×D1312yes—
121C4#8820412yes—
122C2#1171872011yescharacteristic
123C2#1171882911yescharacteristic
124C2#1171884211yescharacteristic
subgroupG/H
centerC22#88194
commutator, cosocleC42×C13C23
FrattiniC42C22×D13
FittingC13×#487C2
socle, prime radicalC22×C13#127
hypercenter#487D13
hypocenterC13#1710
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
99. C13#1710semidirect

Maximal subgroups

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

subgroupindex
C13×#4872
#117187542
#117187422
#117187392
#117183422
C8×#10552
#171013