Finite Group Databasebeta

← C4⋊(#131⋊C3) #73242

Subgroups — C4⋊(#131⋊C3) #73242

Order 384.

134 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 38 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×#131⋊C3C212yesmaximal
2C4×#41⋊C3C211yesmaximal, characteristic
3#2906C311yesmaximal, characteristic, complemented, Sylow
4C2×#41⋊C3C2211yescharacteristic
5#131⋊C3—22no—
6C4×SL(2,𝔽3)C411yescharacteristic
7C4×SL(2,𝔽3)C411yescharacteristic
8C3×C4⋊C8—41nomaximal
9C2×#131C2×C312yes—
10C4×#41C2×C311yescharacteristic
11#424—32no—
12#423—31no—
13C2×C4⋊C8—31no—
14#41⋊C3D411yescharacteristic
15#41⋊C3Q811yescharacteristic
16C2×SL(2,𝔽3)C2×C411yescharacteristic
17C2×C3×C8—42no—
18C3×C42—41no—
19C2×#41C22×C311yescharacteristic
20#131—22no—
21#131—62no—
22C2×M16—32no—
23C22×C8—32no—
24C4×Q8C3×C411yescharacteristic
25C4×Q8C3×C411yescharacteristic
26C4×D4—31no—
27C4×D4—31no—
28#117—31no—
29C2×C42—31no—
30C4⋊C8—32no—
31C4⋊C8—32no—
32C4⋊C8—31no—
33C4⋊C8A411yescharacteristic
34C2×C3×C4—41no—
35C2×C3×C4—41no—
36C2×C3×C4—41no—
37SL(2,𝔽3)C4⋊C411yescharacteristic
38C3×C8—82no—
39#41—31no—
40#41—31no—
41#41C3×D411yescharacteristic
42#41C3×Q811yescharacteristic
43C2×Q8C2×C3×C411yescharacteristic
44C2×D4—31no—
45C22×C4—31no—
46C22×C4—31no—
47C22×C4—31no—
48M16—62no—
49M16—62no—
50C2×C8—32no—
51C2×C8—62no—
52C2×C8—62no—
53C2×C8C2×A412yes—
54C4⋊C4—31no—
55C4⋊C4—31no—
56C22⋊C4—32no—
57C42—31no—
58C42—31no—
59C42—31no—
60C42C2×A411yescharacteristic
61C22×C3—41no—
62C3×C4—42no—
63C3×C4—41no—
64C3×C4—41no—
65C3×C4—81no—
66C23—31no—
67Q8—31no—
68Q8C3×C4⋊C411yescharacteristic
69D4—31no—
70D4—31no—
71D4—32no—
72C2×C4—31no—
73C2×C4—31no—
74C2×C4—31no—
75C2×C4—31no—
76C2×C4—31no—
77C2×C4—31no—
78C2×C4—31no—
79C2×C4—62no—
80C2×C4—121no—
81C2×C4C4×A411yescharacteristic
82C2×C4C4×A411yescharacteristic
83C2×C4C22×A411yescharacteristic
84C8—22no—
85C8—62no—
86C2×C3—41no—
87C2×C3—41no—
88C2×C3—41no—
89C22—31no—
90C22—31no—
91C22—61no—
92C22—61no—
93C22C2×C4×A411yescharacteristic
94C4—21no—
95C4—31no—
96C4—31no—
97C4—61no—
98C4—61no—
99C4#131⋊C312yescomplemented
100C4D4×A411yescharacteristic
101C4Q8×A411yescharacteristic
102C3—41noSylow
103C2—61no—
104C2—61no—
105C2A4×C4⋊C411yescharacteristic
106C2C2×#131⋊C311yescharacteristic
107C2#568⋊C311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×A4
commutatorC2×Q8C2×C3×C4
Fitting#2906C3
socleC22C2×C4×A4
prime radicalC2×#41⋊C3C22
cosocleC2×#41C22×C3
hypercenterC4⋊C8A4
hypocenterQ8C3×C4⋊C4
LCSG ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C2×C4 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
3. #2906C3semidirect
99. C4#131⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×#131⋊C32
C4×#41⋊C32
#29063
C3×C4⋊C84