Finite Group Databasebeta

← #16777069

Subgroups — #16777069

Order 3328.

206 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 62 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#13129877C212yesmaximal
2#13115806C211yesmaximal, characteristic
3C2×C13×#125C411yescharacteristic
4C2×#88106—22no—
5#11718596C411yescharacteristic
6C2×#88043C2211yescharacteristic
7#11718121—22no—
8C13×#125—21no—
9C13×#125—41no—
10C13×#125C812yes—
11C2×C13×C4⋊C4—21no—
12C2×C13×C4⋊C4—41no—
13C2×C42×C13C2×C411yescharacteristic
14C2×C4⋊Dic13—21no—
15C2×C4⋊Dic13—41no—
16C22×#1055D412yes—
17#88106—42no—
18#88106—42no—
19C2×#6092—24no—
20#88043—41no—
21#7130—131nomaximal, Sylow
22C22×C4×C13—21no—
23C22×C4×C13—41no—
24C22×C4×C13C22⋊C411yescharacteristic
25C22×Dic13—41no—
26C13×C4⋊C4—22no—
27C13×C4⋊C4—42no—
28C13×C4⋊C4—42no—
29C13×C4⋊C4—41no—
30C42×C13—21no—
31C42×C13C2×C811yescharacteristic
32C42×C13M1611yescharacteristic
33C4⋊Dic13—42no—
34C4⋊Dic13—82no—
35C2×#1055—22no—
36C2×#1055—22no—
37C2×#1055SD1612yes—
38C2×#1055Q1612yes—
39#6092—44no—
40#1992—131no—
41#1375—132no—
42C23×C13#10011yescharacteristic
43C2×C4×C13—21no—
44C2×C4×C13—21no—
45C2×C4×C13—41no—
46C2×C4×C13—41no—
47C2×C4×C13—42no—
48C2×C4×C13—81no—
49C2×C4×C13—81no—
50C2×C4×C13C22⋊C811yescharacteristic
51C2×C4×C13#9911yescharacteristic
52C2×C4×C13#10312yes—
53C2×C4×C13#10412yes—
54C2×Dic13—82no—
55C2×Dic13—81no—
56#1055—22no—
57#1055—22no—
58C2×#125#26111yescharacteristic
59C2×M32—262no—
60C2×#97—131no—
61#384—131no—
62#340—262no—
63C22×C13—21no—
64C22×C13—21no—
65C22×C13#32311yescharacteristic
66C22×C13#32911yescharacteristic
67C22×C13#33311yescharacteristic
68C4×C13—41no—
69C4×C13—41no—
70C4×C13—82no—
71C4×C13Q8⋊C812yes—
72C4×C13#32812yes—
73Dic13—161no—
74C22×C8—132no—
75#125—21no—
76#125—41no—
77#125#105712yes—
78C2×C4⋊C4—21no—
79C2×C4⋊C4—41no—
80C2×C4⋊C4—261no—
81C2×C4⋊C4—521no—
82C2×C42C2×#26111yescharacteristic
83M32—522no—
84M32—522no—
85C2×C16—264no—
86#97—521no—
87C2×C13—21no—
88C2×C13—21no—
89C2×C13#127211yescharacteristic
90C2×C13#135511yescharacteristic
91C2×C13#135611yescharacteristic
92C22×C4—21no—
93C22×C4—41no—
94C22×C4—521no—
95C22×C4C22⋊#26111yescharacteristic
96C2×C8—132no—
97C2×C8—132no—
98C2×C8—262no—
99C2×C8—262no—
100C4⋊C4—22no—
101C4⋊C4—42no—
102C4⋊C4—42no—
103C4⋊C4—41no—
104C4⋊C4—522no—
105C4⋊C4—1042no—
106C42—21no—
107C42C2×#105711yescharacteristic
108C42#612211yescharacteristic
109C16—524no—
110C13#713011yescharacteristic, complemented, Sylow
111C23#8812111yescharacteristic
112C2×C4—21no—
113C2×C4—21no—
114C2×C4—41no—
115C2×C4—41no—
116C2×C4—42no—
117C2×C4—81no—
118C2×C4—81no—
119C2×C4—1042no—
120C2×C4—1041no—
121C2×C4#8811712yes—
122C2×C4#8811812yes—
123C2×C4#8811911yescharacteristic
124C2×C4C22⋊#105711yescharacteristic
125C8—262no—
126C8—262no—
127C22—21no—
128C22—21no—
129C22#1171829911yescharacteristic
130C22#1171830311yescharacteristic
131C22#1171830511yescharacteristic
132C4—41no—
133C4—41no—
134C4—82no—
135C4—2081no—
136C4#1171829812yes—
137C4Q8⋊#105712yes—
138C2—21no—
139C2—21no—
140C2#1312965611yescharacteristic
141C2#1312983911yescharacteristic
142C2#1312984311yescharacteristic
subgroupG/H
centerC22#11718299
commutatorC42×C13C2×C8
FrattiniC2×C42C2×#261
FittingC2×C13×#125C4
socleC22×C13#329
prime radicalC23×C13#100
cosocleC2×#88043C22
hypercenterC2×#125#261
hypocenterC13#7130
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
110. C13#7130semidirect

Maximal subgroups

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

subgroupindex
#131298772
#131158062
#713013