Finite Group Databasebeta

← #2812⋊C3 #73204

Subgroups — #2812⋊C3 #73204

Order 384.

162 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 20 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×#120⋊C3C212yesmaximal, complemented
2#379⋊C3C211yesmaximal, characteristic, complemented
3#2812C311yesmaximal, characteristic, complemented, Sylow
4C2×C22⋊A4C2211yescharacteristic
5D4×A4—41nomaximal
6#120⋊C3—22no—
7C2×#120C2×C312yescomplemented
8#397—31no—
9#394—32no—
10#392—31no—
11#379C2×C311yescharacteristic, complemented
12C22⋊A4D411yescharacteristic, complemented
13C22×A4—42no—
14C4×A4—41no—
15C25C22×C311yescharacteristic
16C22×D4—32no—
17C22×D4A411yescharacteristic, complemented
18#120—22no—
19#120—62no—
20C2×C4⋊C4—31no—
21C2×C22⋊C4—32no—
22C2×C22⋊C4—32no—
23C2×C22⋊C4—31no—
24C2×C22⋊C4—31no—
25#95—31no—
26#95—31no—
27C2×A4—41no—
28C2×A4—82no—
29C2×A4—161no—
30C3×D4—161no—
31C24—31no—
32C24—31no—
33C24—121no—
34C24—121no—
35C24C3×D411yescharacteristic, complemented
36C24C2×A412yes—
37C2×D4—62no—
38C2×D4—62no—
39C2×D4—121no—
40C2×D4—122no—
41C2×D4—122no—
42C22×C4—32no—
43C22×C4—31no—
44C22×C4C2×A411yescharacteristic
45C4⋊C4—121no—
46C22⋊C4—62no—
47C22⋊C4—62no—
48C22⋊C4—121no—
49C22⋊C4—121no—
50C22⋊C4—122no—
51C22×C3—162no—
52A4—41no—
53A4—161no—
54C3×C4—161no—
55C23—22no—
56C23—31no—
57C23—31no—
58C23—41no—
59C23—62no—
60C23—61no—
61C23—61no—
62C23—62no—
63C23—62no—
64C23—62no—
65C23—121no—
66C23—121no—
67C23—122no—
68C23—121no—
69C23—121no—
70C23—123no—
71C23C22×A411yescharacteristic
72D4—41no—
73D4—121no—
74D4—124no—
75D4—124no—
76C2×C4—61no—
77C2×C4—62no—
78C2×C4—61no—
79C2×C4—62no—
80C2×C4—62no—
81C2×C4—62no—
82C2×C3—161no—
83C2×C3—322no—
84C22—31no—
85C22—31no—
86C22—42no—
87C22—41no—
88C22—62no—
89C22—62no—
90C22—61no—
91C22—61no—
92C22—122no—
93C22—122no—
94C22—122no—
95C22—121no—
96C22—121no—
97C22—121no—
98C22—123no—
99C22—121no—
100C22D4×A411yescharacteristic
101C4—41no—
102C4—121no—
103C4—122no—
104C3—161noSylow
105C2—31no—
106C2—31no—
107C2—82no—
108C2—121no—
109C2—121no—
110C2#545011yescharacteristic
subgroupG/H
center, hypercenterC2#5450
commutator, cosocleC25C22×C3
Frattini, socleC23C22×A4
Fitting#2812C3
hypocenterC24C3×D4
LCSG ▷ C25 ▷ C24
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×#120⋊C3C2semidirect
2. #379⋊C3C2semidirect
3. #2812C3semidirect
7. C2×#120C2×C3semidirect
11. #379C2×C3semidirect
12. C22⋊A4D4semidirect
17. C22×D4A4semidirect
35. C24C3×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#120⋊C32
#379⋊C32
#28123
D4×A44