Finite Group Databasebeta

← #88183⋊C3 #11928294

Subgroups — #88183⋊C3 #11928294

Order 1248.

156 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 55 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
1C22×C4×C13⋊C3C211yesmaximal, characteristic, complemented
2C2×(C22⋊D13)⋊C3C211yesmaximal, characteristic
3(C22⋊Dic13)⋊C3C211yesmaximal, characteristic, complemented
4#6103⋊C3C212yesmaximal, complemented
5#6101⋊C3C212yesmaximal, complemented
6#88183C311yesmaximal, characteristic, complemented, Hall
7C23×C13⋊C3C2211yescharacteristic
8C22×D13⋊C3C2211yescharacteristic
9C2×C4×C13⋊C3—22no—
10C2×C4×C13⋊C3C2212yes—
11(C22⋊D13)⋊C3—22no—
12C2×Dic13⋊C3C2211yescharacteristic
13C2×Dic13⋊C3C2212yes—
14C22×C4×C13C2×C311yescharacteristic, complemented
15C2×C22⋊D13C2×C311yescharacteristic
16C22⋊Dic13C2×C311yescharacteristic, complemented
17#6103C2×C312yescomplemented
18#6101C2×C312yescomplemented
19C22×C13⋊C3—22no—
20C22×C13⋊C3D412yes—
21C22×C13⋊C3C2311yescharacteristic
22C2×D13⋊C3—21no—
23C2×D13⋊C3—22no—
24C4×C13⋊C3—22no—
25Dic13⋊C3—21no—
26Dic13⋊C3—22no—
27C23×C13C22×C311yescharacteristic
28C22×D13C22×C311yescharacteristic
29C2×C4×C13—22no—
30C2×C4×C13C22×C312yes—
31C22⋊D13—22no—
32C2×Dic13C22×C311yescharacteristic
33C2×Dic13C22×C312yes—
34C3×#123—131nomaximal, Hall
35C2×C13⋊C3—22no—
36C2×C13⋊C3C2×D411yescharacteristic
37C2×C13⋊C3#4112yes—
38D13⋊C3—41no—
39C22×C13—22no—
40C22×C13C3×D412yes—
41C22×C13C23×C311yescharacteristic
42C2×D13—21no—
43C2×D13—22no—
44C4×C13—22no—
45Dic13—21no—
46Dic13—22no—
47C2×C3×D4—131no—
48C22×C3×C4—131no—
49C3×C4⋊C4—132no—
50C3×C22⋊C4—132no—
51C3×C22⋊C4—131no—
52C13⋊C3#12311yescharacteristic, complemented, Hall
53#123—131noSylow
54C2×C13—22no—
55C2×C13C2×C3×D411yescharacteristic
56C2×C13C3×#4112yes—
57D13—41no—
58C23×C3—131no—
59C23×C3—131no—
60C3×D4—262no—
61C2×C3×C4—132no—
62C2×C3×C4—131no—
63C2×C3×C4—132no—
64C2×C3×C4—262no—
65C2×D4—131no—
66C22×C4D13⋊C311yescharacteristic, complemented
67C4⋊C4—132no—
68C22⋊C4—131no—
69C22⋊C4—132no—
70C13C3×#12311yescharacteristic, complemented, Sylow
71C22×C3—132no—
72C22×C3—131no—
73C22×C3—262no—
74C22×C3—261no—
75C22×C3—262no—
76C3×C4—262no—
77C3×C4—262no—
78C3×C4—261no—
79C23—131no—
80C23C2×D13⋊C311yescharacteristic
81D4—262no—
82C2×C4—22no—
83C2×C4—132no—
84C2×C4—131no—
85C2×C4C2×D13⋊C312yes—
86C2×C3—132no—
87C2×C3—131no—
88C2×C3—262no—
89C2×C3—521no—
90C22—22no—
91C22—262no—
92C22—261no—
93C22(C22⋊D13)⋊C312yes—
94C22C22×D13⋊C311yescharacteristic
95C4—22no—
96C4—262no—
97C4—261no—
98C3—131noSylow
99C2—22no—
100C2—521no—
101C2#6127⋊C312yes—
102C2C2×(C22⋊D13)⋊C311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D13⋊C3
commutator, socle, cosocleC22×C13C23×C3
FittingC22×C4×C13C2×C3
prime radicalC2×(C22⋊D13)⋊C3C2
hypercenterC22×C4D13⋊C3
hypocenterC13C3×#123
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C13⋊C3C2semidirect
3. (C22⋊Dic13)⋊C3C2semidirect
4. #6103⋊C3C2semidirect
5. #6101⋊C3C2semidirect
6. #88183C3semidirect
14. C22×C4×C13C2×C3semidirect
16. C22⋊Dic13C2×C3semidirect
17. #6103C2×C3semidirect
18. #6101C2×C3semidirect
52. C13⋊C3#123semidirect
66. C22×C4D13⋊C3semidirect
70. C13C3×#123semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C13⋊C32
C2×(C22⋊D13)⋊C32
(C22⋊Dic13)⋊C32
#6103⋊C32
#6101⋊C32
#881833
C3×#12313