Finite Group Databasebeta

← #13113979

Subgroups — #13113979

Order 1664.

218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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#11719439C211yesmaximal, characteristic
2C13×#494C211yesmaximal, characteristic, complemented
3#11718745C212yesmaximal, complemented
4#11718138C211yesmaximal, characteristic, complemented
5#11718051C212yesmaximal, complemented
6C2×C13×Q16—22no—
7C13×C4⋊Q8C2211yescharacteristic
8C13×C4⋊Q8C2211yescharacteristic
9#88201—22no—
10#88149—22no—
11#88146—22no—
12C4×D52C2212yes—
13C4×C8×C13C2211yescharacteristic
14#88049—22no—
15#88048—22no—
16C4⋊#1055C2212yes—
17C2×Q8×C13—21no—
18C2×Q8×C13D412yes—
19C2×D52—22no—
20C2×D52D412yes—
21C2×C4×D13—22no—
22C13×Q16—44no—
23C2×C8×C13—21no—
24C13×C4⋊C4—22no—
25C13×C4⋊C4—22no—
26C42×C13C2311yescharacteristic
27#6103—24no—
28#6103—22no—
29C4⋊Dic13D412yes—
30C4×Dic13—22no—
31C2×#1055—22no—
32#1634—131nomaximal, Sylow
33C22×D13—22no—
34Q8×C13—42no—
35Q8×C13—42no—
36C2×C4×C13—22no—
37C2×C4×C13—41no—
38C2×C4×C13C2×D411yescharacteristic
39C2×C4×C13C2×D412yes—
40C2×Dic13—22no—
41D52—22no—
42D52—22no—
43D52—82no—
44C4×D13—42no—
45C4×D13—42no—
46C8×C13—22no—
47#1055—42no—
48#555—131no—
49#494D1311yescharacteristic, complemented
50#476—132no—
51#333—131no—
52D4⋊C8—132no—
53C22×C13#12011yescharacteristic
54C2×D13—42no—
55C2×D13—42no—
56C2×D13—42no—
57C4×C13—21no—
58C4×C13—42no—
59C4×C13—81no—
60C4×C13#13512yes—
61C4×C13#13712yes—
62Dic13—42no—
63C2×Q16—22no—
64C4⋊Q8C2×D1311yescharacteristic
65C4⋊Q8C2×D1311yescharacteristic
66#124—262no—
67#121—262no—
68C4×D4—132no—
69#117—262no—
70#106—262no—
71C4⋊C8—132no—
72#102—262no—
73C4×C8C2×D1311yescharacteristic
74C2×C13#45212yes—
75C2×C13#45311yescharacteristic
76D13—82no—
77C2×Q8—21no—
78C2×Q8C22⋊D1312yes—
79C2×D4—132no—
80C2×D4—262no—
81C22×C4—262no—
82Q16—44no—
83C2×C8—21no—
84C2×C8—262no—
85C4⋊C4—22no—
86C4⋊C4—22no—
87C4⋊C4—132no—
88C22⋊C4—264no—
89C22⋊C4—262no—
90C42—262no—
91C42C22×D1311yescharacteristic
92C13#163411yescharacteristic, complemented, Sylow
93C23—262no—
94Q8—42no—
95Q8—42no—
96D4—262no—
97D4—262no—
98D4—1042no—
99C2×C4—22no—
100C2×C4—41no—
101C2×C4—262no—
102C2×C4—522no—
103C2×C4—522no—
104C2×C4D4×D1312yes—
105C2×C4C2×C22⋊D1311yescharacteristic
106C8—22no—
107C8—522no—
108C22—522no—
109C22—522no—
110C22—522no—
111C22#8819111yescharacteristic
112C4—21no—
113C4—42no—
114C4—81no—
115C4—522no—
116C4#8817212yes—
117C4#8817312yes—
118C2—1042no—
119C2#1171873811yescharacteristic
120C2#1171884812yes—
subgroupG/H
centerC22#88191
commutator, cosocleC42×C13C23
FrattiniC42C22×D13
FittingC13×#494C2
socleC22×C13#120
prime radical#11719439C2
hypercenter#494D13
hypocenterC13#1634
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
2. C13×#494C2semidirect
3. #11718745C2semidirect
4. #11718138C2semidirect
5. #11718051C2semidirect
49. #494D13semidirect
92. C13#1634semidirect

Maximal subgroups

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

subgroupindex
#117194392
C13×#4942
#117187452
#117181382
#117180512
#163413