Finite Group Databasebeta

← #2380⋊C3 #73179

Subgroups — #2380⋊C3 #73179

Order 384.

148 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 26 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×#127⋊C3C211yesmaximal, characteristic
2#383⋊C3C212yesmaximal, complemented
3#2380C311yesmaximal, characteristic, complemented, Sylow
4C2×C4×A4—41nomaximal
5#127⋊C3C412yescomplemented
6C2×C42⋊C3C2211yescharacteristic
7C2×#127C2×C311yescharacteristic
8#386—31no—
9#386—31no—
10#386—32no—
11#383C2×C312yescomplemented
12C22×A4—41no—
13C4×A4—42no—
14C42⋊C3C2×C411yescharacteristic, complemented
15C22×D4—31no—
16C22×D4—31no—
17C23×C4—31no—
18C23×C4A411yescharacteristic
19#127—32no—
20#127C3×C412yescomplemented
21C2×C22⋊C4—31no—
22C2×C22⋊C4—31no—
23C2×C22⋊C4—32no—
24C2×C42C22×C311yescharacteristic
25#95—32no—
26#95—32no—
27C2×A4—42no—
28C2×A4—41no—
29C2×C3×C4—161no—
30C24—31no—
31C24C2×A411yescharacteristic
32C2×D4—32no—
33C2×D4—32no—
34C2×D4—32no—
35C2×D4—32no—
36C2×D4—121no—
37C2×D4—121no—
38C2×D4—121no—
39C2×D4—121no—
40C22×C4—31no—
41C22×C4—32no—
42C22×C4—121no—
43C22×C4—122no—
44C22×C4—121no—
45C22×C4C2×A412yes—
46C22⋊C4—122no—
47C22⋊C4—121no—
48C22⋊C4—121no—
49C42—31no—
50C42C2×C3×C411yescharacteristic, complemented
51C22×C3—161no—
52A4—41no—
53C3×C4—162no—
54C23—32no—
55C23—61no—
56C23—61no—
57C23—61no—
58C23—62no—
59C23—62no—
60C23—61no—
61C23C4×A412yes—
62C23C22×A411yescharacteristic
63D4—122no—
64D4—122no—
65D4—122no—
66D4—122no—
67C2×C4—31no—
68C2×C4—31no—
69C2×C4—41no—
70C2×C4—62no—
71C2×C4—61no—
72C2×C4—61no—
73C2×C4—62no—
74C2×C4—62no—
75C2×C4—62no—
76C2×C4—121no—
77C2×C4—124no—
78C2×C3—162no—
79C2×C3—161no—
80C22—31no—
81C22—31no—
82C22—41no—
83C22—62no—
84C22—62no—
85C22—64no—
86C22—121no—
87C22—121no—
88C22—122no—
89C22—121no—
90C22C2×C4×A411yescharacteristic
91C4—42no—
92C4—61no—
93C4—61no—
94C4—122no—
95C3—161noSylow
96C2—31no—
97C2—31no—
98C2—42no—
99C2—122no—
100C2#560⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2#560⋊C3
commutator, hypocenterC42C2×C3×C4
Frattini, socleC23C22×A4
Fitting#2380C3
prime radicalC2×#127⋊C3C2
cosocleC2×C42C22×C3
LCSG ▷ C42
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. #383⋊C3C2semidirect
3. #2380C3semidirect
5. #127⋊C3C4semidirect
11. #383C2×C3semidirect
14. C42⋊C3C2×C4semidirect
20. #127C3×C4semidirect
50. C42C2×C3×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#127⋊C32
#383⋊C32
#23803
C2×C4×A44