Finite Group Databasebeta

← #1779⋊C3 #68024

Subgroups — #1779⋊C3 #68024

Order 384.

172 conjugacy classes of subgroups; only the 15 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 15 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
1C4×C22⋊A4C211yesmaximal, characteristic
2#1779C311yesmaximal, characteristic, complemented, Sylow
3C2×C22⋊A4C411yescharacteristic
4C8×A4—41nomaximal
5C24×C4C2×C311yescharacteristic
6C2×C22⋊C8—31no—
7C2×C22⋊C8—31no—
8C22⋊A4C811yescharacteristic, complemented
9C4×A4—41no—
10C4×A4—82no—
11C25C3×C411yescharacteristic
12C23×C4—31no—
13C23×C4—31no—
14C23×C4—62no—
15C23×C4—62no—
16C22×C8—31no—
17C22×C8A411yescharacteristic, complemented
18C22⋊C8—62no—
19C22⋊C8—62no—
20C2×A4—41no—
21C2×A4—82no—
22C3×C8—161no—
23C24—31no—
24C24—31no—
25C24—62no—
26C24—62no—
27C24C3×C811yescharacteristic, complemented
28C22×C4—22no—
29C22×C4—32no—
30C22×C4—32no—
31C22×C4—31no—
32C22×C4—62no—
33C22×C4—62no—
34C22×C4—64no—
35C22×C4—62no—
36C22×C4—62no—
37C22×C4—64no—
38C22×C4—62no—
39C22×C4—62no—
40C22×C4C2×A411yescharacteristic
41C2×C8—61no—
42C2×C8—61no—
43C2×C8—62no—
44A4—41no—
45A4—82no—
46C3×C4—161no—
47C23—22no—
48C23—32no—
49C23—32no—
50C23—31no—
51C23—31no—
52C23—62no—
53C23—62no—
54C23—62no—
55C23—62no—
56C23—62no—
57C23—64no—
58C23—62no—
59C23—62no—
60C23—64no—
61C23C4×A411yescharacteristic
62C2×C4—31no—
63C2×C4—31no—
64C2×C4—32no—
65C2×C4—62no—
66C2×C4—64no—
67C2×C4—62no—
68C2×C4—64no—
69C2×C4—62no—
70C2×C4—62no—
71C2×C4—62no—
72C8—41no—
73C8—121no—
74C2×C3—161no—
75C22—22no—
76C22—31no—
77C22—31no—
78C22—32no—
79C22—32no—
80C22—62no—
81C22—62no—
82C22—62no—
83C22—64no—
84C22—62no—
85C22—62no—
86C22—62no—
87C22—64no—
88C22—62no—
89C22C8×A411yescharacteristic
90C4—31no—
91C4—62no—
92C4#120⋊C311yescharacteristic
93C3—161noSylow
94C2—31no—
95C2—31no—
96C2—62no—
97C2—62no—
98C2#379⋊C311yescharacteristic
subgroupG/H
center, hypercenterC4#120⋊C3
commutator, hypocenterC24C3×C8
FrattiniC22×C4C2×A4
Fitting#1779C3
socleC23C4×A4
prime radicalC2×C22⋊A4C4
cosocleC24×C4C2×C3
LCSG ▷ C24
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. #1779C3semidirect
8. C22⋊A4C8semidirect
17. C22×C8A4semidirect
27. C24C3×C8semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊A42
#17793
C8×A44