Finite Group Databasebeta

← #16777898

Subgroups — #16777898

Order 3328.

150 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 34 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#13129952C211yesmaximal, characteristic, complemented
2#13129904C211yesmaximal, characteristic, complemented
3#13116936C211yesmaximal, characteristic
4#11719092—21no—
5C2×C13×D16C411yescharacteristic, complemented
6#11718818—21no—
7C2×#88038C2211yescharacteristic
8#11718249—21no—
9#11718154—21no—
10#11718097C411yescharacteristic, complemented
11#88237—41no—
12C2×C13×D8—21no—
13#88192—41no—
14C2×C8×D13D411yescharacteristic
15#88102—41no—
16#88101—22no—
17C13×D16—41no—
18C2×C13×C16C2×C411yescharacteristic
19#88072—41no—
20#88058—21no—
21C2×#6090D411yescharacteristic
22#88038—41no—
23#88036—41no—
24#7422—131nomaximal, Sylow
25C2×D4×C13—41no—
26C2×C22⋊D13—81no—
27C2×C4×D13D811yescharacteristic
28C22⋊#261—81no—
29C4⋊#261—42no—
30C4×#261—81no—
31C13×D8—41no—
32C13×D8—41no—
33C2×C8×C13C22⋊C411yescharacteristic
34C22⋊Dic13—81no—
35C4⋊Dic13—41no—
36C2×#1055SD1611yescharacteristic
37C8×D13—21no—
38C8×D13—21no—
39C13×C16—21no—
40#6090—21no—
41#2218—131no—
42#1400—131no—
43#1384—131no—
44C23×C13—81no—
45C22×D13D1611yescharacteristic
46C2×#261—82no—
47D4×C13—81no—
48D4×C13—81no—
49C2×C4×C13#10211yescharacteristic
50C22⋊D13—162no—
51C2×Dic13—81no—
52C2×Dic13SD3211yescharacteristic
53C4×D13—21no—
54C4×D13—21no—
55C8×C13#9911yescharacteristic
56C8×C13#10411yescharacteristic
57#1055—21no—
58C2×D16#26111yescharacteristic, complemented
59C2×M32—131no—
60#466—261no—
61#427—261no—
62M64—261no—
63#367—131no—
64#357—261no—
65C22×C13—161no—
66C22×C13—161no—
67C22×C13—161no—
68C22×C13#35711yescharacteristic
69C2×D13—21no—
70C2×D13—41no—
71#261—162no—
72C4×C13#32711yescharacteristic
73C4×C13#36011yescharacteristic
74Dic13—21no—
75Dic13—161no—
76C2×D8—21no—
77C22×C8—131no—
78#121—521no—
79#117—521no—
80D16—41no—
81M32—521no—
82C2×C16—131no—
83C2×C16C2×#26111yescharacteristic
84#107—261no—
85#107—521no—
86#106—262no—
87#102—521no—
88C32—521no—
89C2×C13—21no—
90C2×C13—321no—
91C2×C13#134711yescharacteristic
92D13—41no—
93C2×D4—41no—
94C2×D4—1041no—
95C22×C4—131no—
96D8—41no—
97D8—41no—
98C2×C8—131no—
99C2×C8—261no—
100C2×C8—261no—
101C2×C8C22⋊#26111yescharacteristic
102C4⋊C4—522no—
103C4⋊C4—521no—
104C22⋊C4—1041no—
105C22⋊C4—1041no—
106C42—1041no—
107C16—21no—
108C16—261no—
109C13#742211yescharacteristic, complemented, Sylow
110C23—81no—
111C23—131no—
112D4—81no—
113D4—81no—
114D4—2082no—
115C2×C4—131no—
116C2×C4—261no—
117C2×C4—261no—
118C2×C4—1042no—
119C2×C4—1041no—
120C2×C4#8811511yescharacteristic
121C8—261no—
122C8#8811611yescharacteristic
123C8#8811911yescharacteristic
124C22—161no—
125C22—161no—
126C22—161no—
127C22—261no—
128C22—521no—
129C22#1171827611yescharacteristic
130C4—261no—
131C4—2081no—
132C4—2082no—
133C4#1171827511yescharacteristic
134C4#1171829211yescharacteristic
135C2—21no—
136C2—321no—
137C2—521no—
138C2#1312982211yescharacteristic
subgroupG/H
centerC2#13129822
commutatorC2×C13×C16C2×C4
FrattiniC2×C16C2×#261
FittingC2×C13×D16C4
socleC2×C13#1347
prime radical#13116936C2
cosocleC2×#88038C22
hypercenterC2×D16#261
hypocenterC13#7422
LCSG ▷ C2×C13×C16 ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. #13129952C2semidirect
2. #13129904C2semidirect
5. C2×C13×D16C4semidirect
10. #11718097C4semidirect
58. C2×D16#261semidirect
109. C13#7422semidirect

Maximal subgroups

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

subgroupindex
#131299522
#131299042
#131169362
#742213