Finite Group Databasebeta

← #88189⋊C3 #11928299

Subgroups — #88189⋊C3 #11928299

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
1C2×D4×C13⋊C3C211yesmaximal, characteristic
2C22×Dic13⋊C3C211yesmaximal, characteristic, complemented
3(C22⋊Dic13)⋊C3C212yesmaximal, complemented
4(C22⋊Dic13)⋊C3C211yesmaximal, characteristic, complemented
5#6101⋊C3C212yesmaximal, complemented
6#88189C311yesmaximal, characteristic, complemented, Hall
7C23×C13⋊C3C2211yescharacteristic
8C23×C13⋊C3C2211yescharacteristic
9D4×C13⋊C3—22no—
10C2×C4×C13⋊C3C2211yescharacteristic
11C2×Dic13⋊C3—22no—
12C2×Dic13⋊C3C2212yes—
13C2×Dic13⋊C3C2212yes—
14C2×D4×C13C2×C311yescharacteristic
15C22×Dic13C2×C311yescharacteristic, complemented
16C22⋊Dic13C2×C311yescharacteristic, complemented
17C22⋊Dic13C2×C312yescomplemented
18#6101C2×C312yescomplemented
19C22×C13⋊C3—22no—
20C22×C13⋊C3—21no—
21C22×C13⋊C3—22no—
22C22×C13⋊C3D412yes—
23C22×C13⋊C3C2311yescharacteristic
24C4×C13⋊C3—21no—
25Dic13⋊C3—22no—
26Dic13⋊C3—22no—
27C23×C13C22×C311yescharacteristic
28C23×C13C22×C311yescharacteristic
29D4×C13—22no—
30C2×C4×C13C22×C311yescharacteristic
31C2×Dic13—22no—
32C2×Dic13C22×C312yes—
33C2×Dic13C22×C312yes—
34C3×#123—131nomaximal, Hall
35C2×C13⋊C3—22no—
36C2×C13⋊C3—41no—
37C2×C13⋊C3C2×D411yescharacteristic
38C2×C13⋊C3#4112yes—
39C22×C13—22no—
40C22×C13—21no—
41C22×C13—22no—
42C22×C13C3×D412yes—
43C22×C13C23×C311yescharacteristic
44C4×C13—21no—
45Dic13—22no—
46Dic13—22no—
47C2×C3×D4—131no—
48C22×C3×C4—131no—
49C3×C4⋊C4—132no—
50C3×C22⋊C4—131no—
51C3×C22⋊C4—132no—
52C13⋊C3#12311yescharacteristic, complemented, Hall
53#123—131noSylow
54C2×C13—22no—
55C2×C13—41no—
56C2×C13C2×C3×D411yescharacteristic
57C2×C13C3×#4112yes—
58C23×C3—131no—
59C23×C3—131no—
60C3×D4—262no—
61C2×C3×C4—132no—
62C2×C3×C4—132no—
63C2×C3×C4—131no—
64C2×C3×C4—262no—
65C2×D4D13⋊C311yescharacteristic
66C22×C4—131no—
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—261no—
77C3×C4—262no—
78C3×C4—262no—
79C23C2×D13⋊C311yescharacteristic
80C23C2×D13⋊C311yescharacteristic
81D4—22no—
82C2×C4—132no—
83C2×C4—132no—
84C2×C4—262no—
85C2×C4C2×D13⋊C311yescharacteristic
86C2×C3—132no—
87C2×C3—131no—
88C2×C3—262no—
89C2×C3—521no—
90C22—22no—
91C22—22no—
92C22—21no—
93C22(C22⋊D13)⋊C312yes—
94C22C22×D13⋊C311yescharacteristic
95C4—21no—
96C4—262no—
97C4—262no—
98C3—131noSylow
99C2—22no—
100C2—41no—
101C2#6129⋊C312yes—
102C2C2×(C22⋊D13)⋊C311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D13⋊C3
commutator, socle, cosocleC22×C13C23×C3
FittingC2×D4×C13C2×C3
prime radicalC2×D4×C13⋊C3C2
hypercenterC2×D4D13⋊C3
hypocenterC13C3×#123
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C22×Dic13⋊C3C2semidirect
3. (C22⋊Dic13)⋊C3C2semidirect
4. (C22⋊Dic13)⋊C3C2semidirect
5. #6101⋊C3C2semidirect
6. #88189C3semidirect
15. C22×Dic13C2×C3semidirect
16. C22⋊Dic13C2×C3semidirect
17. C22⋊Dic13C2×C3semidirect
18. #6101C2×C3semidirect
52. C13⋊C3#123semidirect
70. C13C3×#123semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C13⋊C32
C22×Dic13⋊C32
(C22⋊Dic13)⋊C32
#6101⋊C32
#881893
C3×#12313