Finite Group Databasebeta

← #15749583

Subgroups — #15749583

Order 3328.

132 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 59 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#13112906C211yesmaximal, characteristic
2#13112754C211yesmaximal, characteristic
3C13×#1591C211yesmaximal, characteristic
4C13×#446—21no—
5C4×C13×Q16C411yescharacteristic
6C13×#335C411yescharacteristic
7C13×Q8⋊C8—21no—
8C82×C13C2211yescharacteristic
9C4⋊#6090—21no—
10C4×#6090—21no—
11C2×C13×Q16C811yescharacteristic
12C4×Q8×C13—21no—
13C13×#107C811yescharacteristic
14C13×C4⋊C8—21no—
15C13×C4⋊C8—41no—
16C13×#103—21no—
17C13×#97—41no—
18C4×C8×C13C2×C411yescharacteristic
19C4×C8×C13D411yescharacteristic
20C4×C8×C13D411yescharacteristic
21C2×#6090—22no—
22C2×#6090—41no—
23#7073—131nomaximal, Sylow
24C2×Q8×C13—21no—
25C13×Q16—41no—
26C2×C8×C13—21no—
27C2×C8×C13—41no—
28C2×C8×C13C2×C811yescharacteristic
29C2×C8×C13M1611yescharacteristic
30C2×C8×C13D811yescharacteristic
31C2×C8×C13SD1611yescharacteristic
32C13×C4⋊C4—21no—
33C13×C4⋊C4—41no—
34C42×C13—41no—
35C42×C13C22⋊C411yescharacteristic
36#6090—42no—
37#6090—81no—
38#1591D1311yescharacteristic
39#1370—131no—
40#1312—131no—
41Q8×C13—41no—
42Q8×C13—41no—
43C2×C4×C13—41no—
44C2×C4×C13—41no—
45C2×C4×C13C22⋊C811yescharacteristic
46C2×C4×C13#10211yescharacteristic
47C2×C4×C13#10411yescharacteristic
48C8×C13—22no—
49C8×C13—21no—
50C8×C13—21no—
51C8×C13—21no—
52C8×C13—81no—
53C8×C13SD3211yescharacteristic
54C8×C13Q3211yescharacteristic
55#446—21no—
56C4×Q16Dic1311yescharacteristic
57C4⋊C16—261no—
58C4×C16—261no—
59#335Dic1311yescharacteristic
60Q8⋊C8—21no—
61C82C2×D1311yescharacteristic
62C22×C13D4⋊C811yescharacteristic
63C4×C13—21no—
64C4×C13—81no—
65C4×C13—81no—
66C4×C13#34911yescharacteristic
67C4×C13#35011yescharacteristic
68C4×C13#35811yescharacteristic
69C4×C13#35911yescharacteristic
70C2×Q16#105511yescharacteristic
71C4×Q8—21no—
72C2×C16—262no—
73C2×C16—521no—
74#107#105511yescharacteristic
75C4⋊C8—21no—
76C4⋊C8—41no—
77#103—21no—
78#97—41no—
79C4×C8C2×Dic1311yescharacteristic
80C4×C8C22⋊D1311yescharacteristic
81C4×C8C22⋊D1311yescharacteristic
82C2×C13#133011yescharacteristic
83C2×C13#133211yescharacteristic
84C2×C13#133611yescharacteristic
85C2×Q8—21no—
86Q16—41no—
87C2×C8—21no—
88C2×C8—41no—
89C2×C8C2×#105511yescharacteristic
90C2×C8#609911yescharacteristic
91C2×C8#610411yescharacteristic
92C2×C8#610511yescharacteristic
93C4⋊C4—21no—
94C4⋊C4—41no—
95C42—41no—
96C42C22⋊Dic1311yescharacteristic
97C16—522no—
98C16—1041no—
99C13#707311yescharacteristic, complemented, Sylow
100Q8—41no—
101Q8—41no—
102C2×C4—41no—
103C2×C4—41no—
104C2×C4C22⋊#105511yescharacteristic
105C2×C4#8807211yescharacteristic
106C2×C4#8807711yescharacteristic
107C8—22no—
108C8—21no—
109C8—21no—
110C8—21no—
111C8—81no—
112C8#8806811yescharacteristic
113C8#8806911yescharacteristic
114C22D4⋊#105511yescharacteristic
115C4—21no—
116C4—81no—
117C4—81no—
118C4#1171814511yescharacteristic
119C4#1171815311yescharacteristic
120C4#1171815611yescharacteristic
121C4#1171815911yescharacteristic
122C2#1311279411yescharacteristic
123C2#1311280011yescharacteristic
124C2#1311281211yescharacteristic
subgroupG/H
centerC2×C4#88072
commutatorC2×C8×C13C2×C8
FrattiniC82C2×D13
FittingC13×#1591C2
socle, prime radicalC22×C13D4⋊C8
cosocleC82×C13C22
hypercenter#1591D13
hypocenterC13#7073
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C82 ◁ #1591

Complements

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

NH ≅ G/Ntype
99. C13#7073semidirect

Maximal subgroups

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

subgroupindex
#131129062
#131127542
C13×#15912
#707313