Finite Group Databasebeta

← C2×#396⋊C3 #73185

Subgroups — C2×#396⋊C3 #73185

Order 384.

213 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 213 conjugacy classes of subgroups — too many to draw. Only its 31 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
1#396⋊C3C212yesmaximal, direct product factor
2C2×#95⋊C3C211yesmaximal, characteristic, complemented
3C2×#396C311yesmaximal, characteristic, complemented, Sylow
4C23×A4—41nomaximal
5#95⋊C3C2211yescharacteristic, complemented
6C22×C4⋊C4—31no—
7C22×C22⋊C4—31no—
8#396—32no—
9#396C2×C312yescomplemented
10C2×#95C2×C311yescharacteristic, complemented
11C22×A4—44no—
12C22×A4—41no—
13C22×A4—42no—
14C25A411yescharacteristic
15C23×C4—31no—
16C23×C4—31no—
17C2×C4⋊C4—32no—
18C2×C4⋊C4—32no—
19C2×C4⋊C4—64no—
20C2×C22⋊C4—32no—
21C2×C22⋊C4—32no—
22C2×C22⋊C4—64no—
23#95—31no—
24#95C22×C311yescharacteristic, complemented
25C23×C3—161no—
26C2×A4—44no—
27C2×A4—42no—
28C2×A4—41no—
29C24—61no—
30C24—62no—
31C24—61no—
32C24SL(2,𝔽3)14yes—
33C24C2×A411yescharacteristic
34C24C2×A412yes—
35C22×C4—34no—
36C22×C4—32no—
37C22×C4—31no—
38C22×C4—31no—
39C22×C4—62no—
40C22×C4—61no—
41C22×C4—61no—
42C22×C4—62no—
43C22×C4—62no—
44C22×C4—61no—
45C22×C4—61no—
46C4⋊C4—64no—
47C4⋊C4—64no—
48C22⋊C4—64no—
49C22⋊C4—64no—
50C22×C3—164no—
51C22×C3—162no—
52C22×C3—161no—
53A4—41no—
54C23—32no—
55C23—31no—
56C23—31no—
57C23—41no—
58C23—64no—
59C23—62no—
60C23—62no—
61C23—64no—
62C23—122no—
63C23—121no—
64C23—122no—
65C23C2×SL(2,𝔽3)12yes—
66C23C2×SL(2,𝔽3)14yes—
67C23C22×A411yescharacteristic
68C2×C4—34no—
69C2×C4—62no—
70C2×C4—64no—
71C2×C4—64no—
72C2×C4—62no—
73C2×C4—61no—
74C2×C4—61no—
75C2×C4—61no—
76C2×C4—61no—
77C2×C4—61no—
78C2×C4—61no—
79C2×C4—122no—
80C2×C4—122no—
81C2×C3—164no—
82C2×C3—162no—
83C2×C3—161no—
84C22—31no—
85C22—32no—
86C22—32no—
87C22—32no—
88C22—32no—
89C22—31no—
90C22—31no—
91C22—44no—
92C22—42no—
93C22—64no—
94C22—122no—
95C22—124no—
96C22#126⋊C311yescharacteristic
97C22C22×SL(2,𝔽3)11yescharacteristic
98C4—64no—
99C4—121no—
100C4—121no—
101C3—161noSylow
102C2—31no—
103C2—31no—
104C2—32no—
105C2—44no—
106C2#396⋊C312yesdirect product factor
107C2C2×#126⋊C311yescharacteristic
subgroupG/H
center, hypercenterC22#126⋊C3
commutator, cosocle, hypocenter#95C22×C3
FrattiniC23C22×A4
FittingC2×#396C3
socleC24C2×A4
LCSG ▷ #95
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. #396⋊C3C2direct (N × H)
2. C2×#95⋊C3C2semidirect
3. C2×#396C3semidirect
5. #95⋊C3C22semidirect
9. #396C2×C3semidirect
10. C2×#95C2×C3semidirect
24. #95C22×C3semidirect
106. C2#396⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
#396⋊C32
C2×#95⋊C32
C2×#3963
C23×A44