Finite Group Databasebeta

← #2375⋊C3 #73178

Subgroups — #2375⋊C3 #73178

Order 384.

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

normal subgroups only

This group has 158 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×#120⋊C3C211yesmaximal, characteristic
2#379⋊C3C212yesmaximal, complemented
3#2375C311yesmaximal, characteristic, complemented, Sylow
4C2×C22⋊A4C2211yescharacteristic
5C2×C4×A4—41nomaximal
6#120⋊C3C412yescomplemented
7C2×#120C2×C311yescharacteristic
8#390—31no—
9#388—32no—
10#386—31no—
11#379C2×C312yescomplemented
12C22⋊A4C2×C411yescharacteristic, complemented
13C22×A4—41no—
14C4×A4—42no—
15C25C22×C311yescharacteristic
16C22×D4—31no—
17C23×C4A411yescharacteristic, complemented
18#120—32no—
19#120C3×C412yescomplemented
20C2×C4⋊C4—31no—
21C2×C22⋊C4—31no—
22C2×C22⋊C4—31no—
23C2×C22⋊C4—32no—
24C2×C22⋊C4—32no—
25C2×C42—31no—
26#95—32no—
27C2×A4—42no—
28C2×A4—41no—
29C2×A4—161no—
30C2×C3×C4—161no—
31C24—31no—
32C24—31no—
33C24—121no—
34C24—121no—
35C24C2×C3×C411yescharacteristic, complemented
36C24C2×A411yescharacteristic
37C2×D4—32no—
38C2×D4—32no—
39C2×D4—121no—
40C2×D4—121no—
41C22×C4—31no—
42C22×C4—32no—
43C22×C4—121no—
44C22×C4C2×A412yes—
45C4⋊C4—121no—
46C22⋊C4—32no—
47C22⋊C4—32no—
48C22⋊C4—122no—
49C22⋊C4—122no—
50C22⋊C4—121no—
51C42—121no—
52C22×C3—161no—
53A4—41no—
54A4—161no—
55C3×C4—162no—
56C23—31no—
57C23—31no—
58C23—41no—
59C23—61no—
60C23—61no—
61C23—62no—
62C23—62no—
63C23—61no—
64C23—61no—
65C23—121no—
66C23—121no—
67C23—121no—
68C23—122no—
69C23—121no—
70C23—123no—
71C23C4×A412yes—
72C23C22×A411yescharacteristic
73D4—122no—
74D4—122no—
75C2×C4—32no—
76C2×C4—41no—
77C2×C4—62no—
78C2×C4—61no—
79C2×C4—61no—
80C2×C4—62no—
81C2×C4—62no—
82C2×C4—62no—
83C2×C4—121no—
84C2×C3—162no—
85C2×C3—161no—
86C22—31no—
87C22—31no—
88C22—41no—
89C22—41no—
90C22—62no—
91C22—61no—
92C22—61no—
93C22—62no—
94C22—62no—
95C22—121no—
96C22—121no—
97C22—122no—
98C22—121no—
99C22—121no—
100C22—123no—
101C22—121no—
102C22C2×C4×A411yescharacteristic
103C4—42no—
104C4—62no—
105C4—122no—
106C3—161noSylow
107C2—31no—
108C2—31no—
109C2—42no—
110C2—121no—
111C2—121no—
112C2#545011yescharacteristic
subgroupG/H
center, hypercenterC2#5450
commutator, hypocenterC24C2×C3×C4
Frattini, socleC23C22×A4
Fitting#2375C3
prime radicalC2×#120⋊C3C2
cosocleC25C22×C3
LCSG ▷ C24
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. #379⋊C3C2semidirect
3. #2375C3semidirect
6. #120⋊C3C4semidirect
11. #379C2×C3semidirect
12. C22⋊A4C2×C4semidirect
17. C23×C4A4semidirect
19. #120C3×C4semidirect
35. C24C2×C3×C4semidirect

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
#23753
C2×C4×A44