Finite Group Databasebeta

← #15749652

Subgroups — #15749652

Order 3328.

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

normal subgroups only

This group has 142 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#13112906C211yesmaximal, characteristic
3C13×#1713C211yesmaximal, characteristic
4C13×#500—21no—
5C13×#500C412yes—
6C13×#494—21no—
7C82×C13C2211yescharacteristic
8C4⋊#6090—21no—
9C4⋊#6090—21no—
10C2×C13×Q16—41no—
11C2×C13×Q16—41no—
12C13×C4⋊Q8—22no—
13C13×#107—41no—
14C13×#107—41no—
15C13×#107—42no—
16C4×C8×C13C2×C411yescharacteristic
17C4×C8×C13D411yescharacteristic
18C4×C8×C13D411yescharacteristic
19C2×#6090—41no—
20C2×#6090—41no—
21#7097—131nomaximal, Sylow
22C2×Q8×C13—42no—
23C13×Q16—82no—
24C13×Q16—81no—
25C13×Q16—81no—
26C2×C8×C13—21no—
27C2×C8×C13D811yescharacteristic
28C2×C8×C13D811yescharacteristic
29C2×C8×C13SD1611yescharacteristic
30C2×C8×C13SD1611yescharacteristic
31C13×C4⋊C4—42no—
32C13×C4⋊C4—42no—
33C42×C13C22⋊C411yescharacteristic
34#6090—81no—
35#6090—81no—
36#1713D1311yescharacteristic
37#1370—131no—
38#1370—131no—
39Q8×C13—82no—
40Q8×C13—82no—
41C2×C4×C13—82no—
42C2×C4×C13#10011yescharacteristic
43C2×C4×C13#10211yescharacteristic
44C2×C4×C13#10211yescharacteristic
45C8×C13—22no—
46C8×C13—21no—
47C8×C13—21no—
48C8×C13D1611yescharacteristic
49C8×C13SD3211yescharacteristic
50C8×C13SD3211yescharacteristic
51C8×C13Q3211yescharacteristic
52#500—21no—
53#500Dic1312yes—
54#494—21no—
55C4⋊C16—261no—
56C4⋊C16—261no—
57C82C2×D1311yescharacteristic
58C22×C13#33111yescharacteristic
59C4×C13—21no—
60C4×C13—162no—
61C4×C13#35711yescharacteristic
62C4×C13#35811yescharacteristic
63C4×C13#36111yescharacteristic
64C4×C13#36211yescharacteristic
65C2×Q16—41no—
66C2×Q16—41no—
67C4⋊Q8—22no—
68C2×C16—521no—
69C2×C16—521no—
70#107—41no—
71#107—41no—
72#107—42no—
73C4×C8C2×Dic1311yescharacteristic
74C4×C8C22⋊D1311yescharacteristic
75C4×C8C22⋊D1311yescharacteristic
76C2×C13#135811yescharacteristic
77C2×C13#136111yescharacteristic
78C2×C13#136211yescharacteristic
79C2×Q8—42no—
80Q16—82no—
81Q16—81no—
82Q16—81no—
83C2×C8—21no—
84C2×C8#610411yescharacteristic
85C2×C8#610411yescharacteristic
86C2×C8#610511yescharacteristic
87C2×C8#610511yescharacteristic
88C4⋊C4—42no—
89C4⋊C4—42no—
90C42C22⋊Dic1311yescharacteristic
91C16—1041no—
92C16—1041no—
93C13#709711yescharacteristic, complemented, Sylow
94Q8—82no—
95Q8—82no—
96C2×C4—82no—
97C2×C4#8807211yescharacteristic
98C2×C4#8807211yescharacteristic
99C2×C4#8807311yescharacteristic
100C8—22no—
101C8—21no—
102C8—21no—
103C8#8806611yescharacteristic
104C8#8806711yescharacteristic
105C8#8806811yescharacteristic
106C8#8806911yescharacteristic
107C22#1171813611yescharacteristic
108C4—21no—
109C4—162no—
110C4#1171815411yescharacteristic
111C4#1171815511yescharacteristic
112C4#1171815611yescharacteristic
113C4#1171815711yescharacteristic
114C2#1311287511yescharacteristic
115C2#1311288211yescharacteristic
116C2#1311288511yescharacteristic
subgroupG/H
centerC22#11718136
commutatorC4×C8×C13C2×C4
FrattiniC82C2×D13
FittingC13×#1713C2
socle, prime radicalC22×C13#331
cosocleC82×C13C22
hypercenter#1713D13
hypocenterC13#7097
LCSG ▷ C4×C8×C13 ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C82 ◁ #1713

Complements

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

NH ≅ G/Ntype
93. C13#7097semidirect

Maximal subgroups

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

subgroupindex
#131129062
C13×#17132
#709713