Finite Group Databasebeta

← #16777816

Subgroups — #16777816

Order 3328.

118 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 118 conjugacy classes of subgroups — too many to draw. Only its 42 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#13129944C211yesmaximal, characteristic, complemented
2#13129871C211yesmaximal, characteristic, complemented
3#13116717C211yesmaximal, characteristic
4C13×#508C411yescharacteristic
5#11718857—21no—
6#11718261—21no—
7C2×#88036—21no—
8#11718159—21no—
9#11718098C411yescharacteristic
10C16×Dic13C2211yescharacteristic
11C13×#135—21no—
12#88202—41no—
13#88106—41no—
14C13×Q32C811yescharacteristic
15C13×SD32—21no—
16C13×D16C811yescharacteristic
17C2×C13×C16C2×C411yescharacteristic
18#88077—41no—
19#88059—21no—
20C8×Dic13D411yescharacteristic
21C2×#6090D411yescharacteristic
22#88036—22no—
23#7388—131nomaximal, Sylow
24C13×#41—41no—
25C13×Q16—21no—
26C13×SD16—41no—
27C13×D8—21no—
28C2×C8×C13C22⋊C411yescharacteristic
29C4×Dic13SD1611yescharacteristic
30#6099—41no—
31#6099—81no—
32C2×#1055—81no—
33C2×#1055D811yescharacteristic
34#6092—81no—
35C13×C16C2×C811yescharacteristic
36C13×C16M1611yescharacteristic
37#6090—21no—
38#2178—131no—
39#1397—131no—
40#1373—131no—
41Q8×C13—41no—
42D4×C13—41no—
43D4×C13—81no—
44C2×C4×C13—81no—
45C2×C4×C13#10211yescharacteristic
46C2×Dic13—21no—
47C8×C13C22⋊C811yescharacteristic
48C8×C13#10411yescharacteristic
49#1055—81no—
50#1055D1611yescharacteristic
51#1055SD3211yescharacteristic
52#508#26111yescharacteristic
53#443—261no—
54C2×C32—261no—
55#368—131no—
56#364—261no—
57#359—261no—
58C4×C16—131no—
59C22×C13—81no—
60C22×C13#35911yescharacteristic
61C4×C13—81no—
62C4×C13D4⋊C811yescharacteristic
63C4×C13#35711yescharacteristic
64Dic13—41no—
65#135—21no—
66#131—521no—
67Q32#105711yescharacteristic
68SD32—21no—
69D16#105711yescharacteristic
70M32—521no—
71C2×C16—131no—
72C2×C16C2×#26111yescharacteristic
73#108—261no—
74#104—521no—
75C4×C8—131no—
76C32—262no—
77C2×C13—21no—
78C2×C13—161no—
79C2×C13#133111yescharacteristic
80#41—41no—
81Q16—21no—
82SD16—41no—
83D8—21no—
84M16—521no—
85M16—1041no—
86C2×C8—131no—
87C2×C8—1041no—
88C2×C8C22⋊#26111yescharacteristic
89C42—131no—
90C16—261no—
91C16—1041no—
92C16C2×#105711yescharacteristic
93C16#612211yescharacteristic
94C13#738811yescharacteristic, complemented, Sylow
95Q8—41no—
96D4—41no—
97D4—81no—
98C2×C4—81no—
99C2×C4—261no—
100C2×C4#8811511yescharacteristic
101C8—131no—
102C8—131no—
103C8—1041no—
104C8#8811611yescharacteristic
105C8C22⋊#105711yescharacteristic
106C22—81no—
107C22#1171827711yescharacteristic
108C4—81no—
109C4—521no—
110C4#1171827611yescharacteristic
111C4D4⋊#105711yescharacteristic
112C2—21no—
113C2—161no—
114C2#1312979011yescharacteristic
subgroupG/H
centerC4#11718276
commutatorC13×C16C2×C8
FrattiniC2×C16C2×#261
Fitting, prime radicalC13×#508C4
socleC2×C13#1331
cosocleC16×Dic13C22
hypercenter#508#261
hypocenterC13#7388
LCSG ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #13129944C2semidirect
2. #13129871C2semidirect
94. C13#7388semidirect

Maximal subgroups

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

subgroupindex
#131299442
#131298712
#131167172
#738813