Finite Group Databasebeta

← #13129961

Subgroups — #13129961

Order 1664.

106 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 106 conjugacy classes of subgroups — too many to draw. Only its 20 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#11718907C211yesmaximal, characteristic
2#11718303C211yesmaximal, characteristic, complemented
3#11718301C211yesmaximal, characteristic, complemented
4C13×2−1+4C411yescharacteristic
5#88205—21no—
6#88198C2211yescharacteristic
7#88113—21no—
8#88112—21no—
9#88077—21no—
10#88076C411yescharacteristic
11C13×#41—21no—
12C13×#41—41no—
13C13×#41—41no—
14C2×Q8×C13—41no—
15C2×Q8×C13C2×C411yescharacteristic
16C2×Dic26D411yescharacteristic
17#6122—41no—
18C2×#1057—41no—
19#6107—41no—
20#6105—41no—
21#6101—41no—
22C4×Dic13D411yescharacteristic
23#6099—21no—
24#1405—131nomaximal, Sylow
25Q8×C13—21no—
26Q8×C13—41no—
27Q8×C13—41no—
28D4×C13—21no—
29D4×C13—41no—
30D4×C13—41no—
31C2×C4×C13—21no—
32C2×C4×C13—41no—
33C2×C4×C13—42no—
34C2×C4×C13C22⋊C411yescharacteristic
35C2×Dic13—21no—
36C2×Dic13—21no—
37Dic26—41no—
38#1057—81no—
39#1057—81no—
40#1055—41no—
41#456—131no—
42#356—131no—
43#333—131no—
44C22×C13—41no—
45C22×C13#9911yescharacteristic
46C4×C13—21no—
47C4×C13—41no—
48C4×C13—41no—
49Dic13—21no—
50Dic13—21no—
51Dic13—41no—
522−1+4#26111yescharacteristic
53#137—261no—
54C4⋊Q8—131no—
55C4⋊C8—261no—
56#104—261no—
57#101—131no—
58#101—261no—
59C2×C13—21no—
60C2×C13—81no—
61C2×C13AΣL(1,𝔽16)11yescharacteristic
62#41—21no—
63#41—41no—
64#41—41no—
65C2×Q8—41no—
66C2×Q8—131no—
67C2×Q8C2×#26111yescharacteristic
68Q16—521no—
69SD16—521no—
70M16—261no—
71M16—521no—
72C2×C8—521no—
73C4⋊C4—521no—
74C42—131no—
75C13#140511yescharacteristic, complemented, Sylow
76Q8—21no—
77Q8—41no—
78Q8—41no—
79Q8—521no—
80D4—21no—
81D4—41no—
82D4—41no—
83C2×C4—21no—
84C2×C4—41no—
85C2×C4—42no—
86C2×C4—261no—
87C2×C4—261no—
88C2×C4C22⋊#26111yescharacteristic
89C8—521no—
90C8—1041no—
91C8—1041no—
92C22—41no—
93C22#8811911yescharacteristic
94C4—21no—
95C4—41no—
96C4—41no—
97C4—261no—
98C4—261no—
99C4—521no—
100C2—21no—
101C2—81no—
102C2#1171830611yescharacteristic
subgroupG/H
centerC2#11718306
commutatorC2×Q8×C13C2×C4
FrattiniC2×Q8C2×#261
Fitting, prime radicalC13×2−1+4C4
socleC2×C13AΣL(1,𝔽16)
cosocle#88198C22
hypercenter2−1+4#261
hypocenterC13#1405
LCSG ▷ C2×Q8×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8 ◁ 2−1+4

Complements

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

NH ≅ G/Ntype
2. #11718303C2semidirect
3. #11718301C2semidirect
75. C13#1405semidirect

Maximal subgroups

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

subgroupindex
#117189072
#117183032
#117183012
#140513