Finite Group Databasebeta

← C2×#395⋊C3 #73183

Subgroups — C2×#395⋊C3 #73183

Order 384.

193 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 193 conjugacy classes of subgroups — too many to draw. Only its 23 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×C22⋊SL(2,𝔽3)C211yesmaximal, characteristic
2#395⋊C3C212yesmaximal, direct product factor
3C2×#395C311yesmaximal, characteristic, complemented, Sylow
4C22⋊SL(2,𝔽3)C2211yescharacteristic
5C2×C4×A4—41nomaximal
6C23×Q8C2×C311yescharacteristic
7C22×C4⋊C4—31no—
8#395—32no—
9#395C2×C312yescomplemented
10C2×#95—31no—
11C22×A4—41no—
12C2×SL(2,𝔽3)—82no—
13C4×A4—42no—
14C22×Q8—31no—
15C22×Q8—62no—
16C22×Q8—62no—
17C22×Q8C22×C311yescharacteristic
18C23×C4—31no—
19C23×C4—31no—
20C23×C4A411yescharacteristic
21C2×C4⋊C4—32no—
22C2×C4⋊C4—32no—
23C2×C4⋊C4—62no—
24C2×C4⋊C4—62no—
25#95—32no—
26#95—32no—
27C2×A4—42no—
28C2×A4—41no—
29C2×C3×C4—161no—
30SL(2,𝔽3)—82no—
31C24C2×A411yescharacteristic
32C2×Q8—22no—
33C2×Q8—62no—
34C2×Q8—62no—
35C2×Q8—64no—
36C2×Q8—62no—
37C2×Q8—62no—
38C2×Q8—64no—
39C2×Q8—62no—
40C22×C4—32no—
41C22×C4—32no—
42C22×C4—34no—
43C22×C4—32no—
44C22×C4—31no—
45C22×C4—31no—
46C22×C4—61no—
47C22×C4—61no—
48C22×C4—61no—
49C22×C4—62no—
50C22×C4—62no—
51C22×C4—62no—
52C22×C4—61no—
53C22×C4C2×A412yes—
54C4⋊C4—64no—
55C4⋊C4—64no—
56C22×C3—161no—
57A4—41no—
58C3×C4—162no—
59C23—31no—
60C23—32no—
61C23—31no—
62C23#41⋊C312yes—
63C23C22×A411yescharacteristic
64Q8—22no—
65Q8—62no—
66Q8—62no—
67Q8—62no—
68Q8—64no—
69C2×C4—32no—
70C2×C4—32no—
71C2×C4—34no—
72C2×C4—41no—
73C2×C4—62no—
74C2×C4—62no—
75C2×C4—64no—
76C2×C4—64no—
77C2×C4—62no—
78C2×C4—64no—
79C2×C4—62no—
80C2×C4—62no—
81C2×C4—62no—
82C2×C4—62no—
83C2×C4—121no—
84C2×C3—162no—
85C2×C3—161no—
86C22—31no—
87C22—32no—
88C22—32no—
89C22—32no—
90C22—32no—
91C22—31no—
92C22—31no—
93C22#120⋊C311yescharacteristic
94C22C2×#41⋊C311yescharacteristic
95C4—42no—
96C4—64no—
97C4—62no—
98C4—62no—
99C3—161noSylow
100C2—31no—
101C2—31no—
102C2—32no—
103C2#395⋊C312yesdirect product factor
104C2C2×#120⋊C311yescharacteristic
subgroupG/H
center, hypercenterC22#120⋊C3
commutator, cosocle, hypocenterC22×Q8C22×C3
FrattiniC23C22×A4
FittingC2×#395C3
socleC24C2×A4
prime radicalC2×C22⋊SL(2,𝔽3)C2
LCSG ▷ C22×Q8
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. #395⋊C3C2direct (N × H)
3. C2×#395C3semidirect
9. #395C2×C3semidirect
103. C2#395⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C22⋊SL(2,𝔽3)2
#395⋊C32
C2×#3953
C2×C4×A44