Finite Group Databasebeta

← #16777820

Subgroups — #16777820

Order 3328.

118 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 118 conjugacy classes of subgroups — too many to draw. Only its 38 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#13129948C211yesmaximal, characteristic, complemented
2#13129861C211yesmaximal, characteristic, complemented
3#13116721C211yesmaximal, characteristic
4#11718565C411yescharacteristic
5#11718556—21no—
6#11718253—21no—
7#11718249—21no—
8C13×#368C411yescharacteristic
9#11718094C2211yescharacteristic
10#11718089—21no—
11#88161—41no—
12#88158—21no—
13C4⋊#1057—41no—
14C2×C13×C16C2×C411yescharacteristic
15C13×#108—21no—
16#88065—41no—
17C8×Dic13D411yescharacteristic
18C2×#6090D411yescharacteristic
19Dic104C811yescharacteristic, complemented
20#88040—21no—
21D208C811yescharacteristic, complemented
22#88036—22no—
23#7389—131nomaximal, Sylow
24#6127—41no—
25C2×#1057—81no—
26C13×M16—41no—
27C2×C8×C13C22⋊C411yescharacteristic
28C4×Dic13D811yescharacteristic
29C2×#1055SD1611yescharacteristic
30Dic52—21no—
31D104—21no—
32#6095—41no—
33#6094—81no—
34C8×D13—81no—
35C13×C16C2×C811yescharacteristic
36C13×C16M1611yescharacteristic
37#6090—21no—
38#2179—131no—
39#1398—131no—
40#1368—131no—
41C2×C4×C13#10211yescharacteristic
42C22⋊D13—81no—
43C2×Dic13—21no—
44D52—41no—
45C4×D13—81no—
46Dic26—41no—
47#1057—161no—
48C8×C13—81no—
49C8×C13C22⋊C811yescharacteristic
50C8×C13#10411yescharacteristic
51#1055—21no—
52#508—131no—
53#443—261no—
54M64—261no—
55#368#26111yescharacteristic
56#359—261no—
57#346—131no—
58#334—261no—
59C22×C13#36011yescharacteristic
60C2×D13—81no—
61C4×C13D4⋊C811yescharacteristic
62C4×C13#36111yescharacteristic
63Dic13—41no—
64Dic13—81no—
65#135—261no—
66#131—521no—
67Q32—131no—
68SD32—261no—
69D16—131no—
70C2×C16—131no—
71C2×C16C2×#26111yescharacteristic
72#108—21no—
73C4⋊C8—521no—
74#104—521no—
75C4×C8—131no—
76C32—262no—
77C2×C13—21no—
78C2×C13#133311yescharacteristic
79D13—161no—
80#41—521no—
81Q16—261no—
82SD16—521no—
83D8—261no—
84M16—41no—
85M16—1041no—
86C2×C8—131no—
87C2×C8—1041no—
88C2×C8—1041no—
89C2×C8C22⋊#26111yescharacteristic
90C42—131no—
91C16—261no—
92C16D13⋊C811yescharacteristic
93C16#611811yescharacteristic
94C13#738911yescharacteristic, complemented, Sylow
95Q8—521no—
96D4—521no—
97D4—1041no—
98C2×C4—261no—
99C2×C4—1041no—
100C2×C4#8811511yescharacteristic
101C8—81no—
102C8—261no—
103C8—2081no—
104C8#8811111yescharacteristic
105C8#8811811yescharacteristic
106C22—1041no—
107C22#1171827911yescharacteristic
108C4—521no—
109C4—1041no—
110C4#1171824311yescharacteristic
111C4#1171827811yescharacteristic
112C2—21no—
113C2—2081no—
114C2#1312979511yescharacteristic
subgroupG/H
centerC2#13129795
commutatorC13×C16C2×C8
FrattiniC2×C16C2×#261
FittingC13×#368C4
socleC2×C13#1333
prime radical#11718565C4
cosocle#11718094C22
hypercenter#368#261
hypocenterC13#7389
LCSG ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #368

Complements

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

NH ≅ G/Ntype
1. #13129948C2semidirect
2. #13129861C2semidirect
19. Dic104C8semidirect
21. D208C8semidirect
94. C13#7389semidirect

Maximal subgroups

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

subgroupindex
#131299482
#131298612
#131167212
#738913