Finite Group Databasebeta

← C3×#1348 #67908

Subgroups — C3×#1348 #67908

Order 384.

116 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 116 conjugacy classes of subgroups — too many to draw. Only its 44 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
1C3×#467C211yesmaximal, characteristic
2C3×C22⋊C16C211yesmaximal, characteristic
3C3×#340C211yesmaximal, characteristic
4#1348C311yesmaximal, characteristic, direct product factor, Sylow
5C2×C3×Q16C411yescharacteristic, complemented
6C22×C3×C8C2211yescharacteristic
7C3×C22⋊Q8—21no—
8C2×C3×C4⋊C4—21no—
9C2×C3×C16—21no—
10C3×#107C411yescharacteristic, complemented
11C3×#103—21no—
12#467C2×C311yescharacteristic
13C22⋊C16C2×C311yescharacteristic
14#340C2×C311yescharacteristic
15C2×C3×Q8—21no—
16C22×C3×C4—41no—
17C22×C3×C4D411yescharacteristic
18C3×Q16—41no—
19C2×C3×C8—41no—
20C2×C3×C8C2×C411yescharacteristic
21C2×C3×C8D411yescharacteristic
22C3×C4⋊C4—22no—
23C3×C4⋊C4—21no—
24C3×C4⋊C4—41no—
25C3×C4⋊C4—41no—
26C3×C22⋊C4—41no—
27C3×C16—41no—
28C2×Q16C3×C411yescharacteristic, complemented
29C22×C8C22×C311yescharacteristic
30C22⋊Q8—21no—
31C2×C4⋊C4—21no—
32C2×C16—21no—
33#107C3×C411yescharacteristic, complemented
34#103—21no—
35C23×C3D811yescharacteristic
36C3×Q8—41no—
37C3×Q8—41no—
38C2×C3×C4—21no—
39C2×C3×C4—21no—
40C2×C3×C4—42no—
41C2×C3×C4—41no—
42C2×C3×C4—41no—
43C2×C3×C4—81no—
44C2×C3×C4—81no—
45C2×C3×C4C22⋊C411yescharacteristic
46C2×C3×C4SD1611yescharacteristic
47C3×C8—21no—
48C3×C8—21no—
49C2×Q8—21no—
50C22×C4—41no—
51C22×C4C3×D411yescharacteristic
52Q16—41no—
53C2×C8—41no—
54C2×C8C2×C3×C411yescharacteristic
55C2×C8C3×D411yescharacteristic
56C4⋊C4—22no—
57C4⋊C4—21no—
58C4⋊C4—41no—
59C4⋊C4—41no—
60C22⋊C4—41no—
61C16—41no—
62C22×C3—21no—
63C22×C3—21no—
64C22×C3#10211yescharacteristic
65C22×C3SD3211yescharacteristic
66C22×C3Q3211yescharacteristic
67C3×C4—21no—
68C3×C4—82no—
69C3×C4—81no—
70C3×C4—81no—
71C3×C4#9911yescharacteristic
72C3×C4#10411yescharacteristic
73C23C3×D811yescharacteristic
74Q8—41no—
75Q8—41no—
76C2×C4—21no—
77C2×C4—21no—
78C2×C4—42no—
79C2×C4—41no—
80C2×C4—41no—
81C2×C4—81no—
82C2×C4—81no—
83C2×C4C3×C22⋊C411yescharacteristic
84C2×C4C3×SD1611yescharacteristic
85C8—21no—
86C8—21no—
87C2×C3—21no—
88C2×C3—21no—
89C2×C3#32711yescharacteristic
90C2×C3#35811yescharacteristic
91C2×C3#36011yescharacteristic
92C22—21no—
93C22—21no—
94C22C3×#10211yescharacteristic
95C22C3×SD3211yescharacteristic
96C22C3×Q3211yescharacteristic
97C4—21no—
98C4—82no—
99C4—81no—
100C4—81no—
101C4C3×#9911yescharacteristic
102C4C3×#10411yescharacteristic
103C3#134811yescharacteristic, direct product factor, Sylow
104C2—21no—
105C2—21no—
106C2C3×#32711yescharacteristic
107C2C3×#35811yescharacteristic
108C2C3×#36011yescharacteristic
subgroupG/H
center, socleC22×C3#102
commutatorC2×C8C2×C3×C4
Frattini, cosocleC22×C8C22×C3
prime radicalC23×C3D8
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×C8 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1348C3direct (N × H)
5. C2×C3×Q16C4semidirect
10. C3×#107C4semidirect
28. C2×Q16C3×C4semidirect
33. #107C3×C4semidirect
103. C3#1348direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#4672
C3×C22⋊C162
C3×#3402
#13483