Finite Group Databasebeta

← C3×#1407 #67967

Subgroups — C3×#1407 #67967

Order 384.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#497C211yesmaximal, characteristic
2C3×#355C211yesmaximal, characteristic
3C3×#354C211yesmaximal, characteristic
4#1407C311yesmaximal, characteristic, direct product factor, Sylow
5C2×C3×Q16—21no—
6C2×C3×SD16—21no—
7C3×C4⋊Q8C411yescharacteristic, complemented
8C3×#124C2211yescharacteristic
9C3×#101—21no—
10C3×#99—21no—
11C3×#97C411yescharacteristic, complemented
12#497C2×C311yescharacteristic
13#355C2×C311yescharacteristic
14#354C2×C311yescharacteristic
15C2×C3×Q8—21no—
16C2×C3×Q8D411yescharacteristic
17C2×C3×D4D411yescharacteristic
18C3×Q16—42no—
19C3×SD16—42no—
20C3×M16—41no—
21C2×C3×C8—21no—
22C3×C4⋊C4—41no—
23C3×C22⋊C4—41no—
24C3×C22⋊C4—41no—
25C3×C42C2×C411yescharacteristic
26C2×Q16—21no—
27C2×SD16—21no—
28C4⋊Q8C3×C411yescharacteristic, complemented
29#124C22×C311yescharacteristic
30#101—21no—
31#99—21no—
32#97C3×C411yescharacteristic, complemented
33C23×C3—21no—
34C3×Q8—41no—
35C3×Q8—41no—
36C3×Q8—41no—
37C3×D4—41no—
38C2×C3×C4—21no—
39C2×C3×C4—21no—
40C2×C3×C4—41no—
41C2×C3×C4—81no—
42C2×C3×C4C22⋊C411yescharacteristic
43C3×C8—22no—
44C3×C8—81no—
45C2×Q8—21no—
46C2×Q8C3×D411yescharacteristic
47C2×D4C3×D411yescharacteristic
48Q16—42no—
49SD16—42no—
50M16—41no—
51C2×C8—21no—
52C4⋊C4—41no—
53C22⋊C4—41no—
54C22⋊C4—41no—
55C42C2×C3×C411yescharacteristic
56C22×C3—41no—
57C22×C3—81no—
58C22×C3#9911yescharacteristic
59C3×C4—21no—
60C3×C4—41no—
61C3×C4—41no—
62C3×C4—81no—
63C3×C4—161no—
64C23—21no—
65Q8—41no—
66Q8—41no—
67Q8—41no—
68D4—41no—
69C2×C4—21no—
70C2×C4—21no—
71C2×C4—41no—
72C2×C4—81no—
73C2×C4C3×C22⋊C411yescharacteristic
74C8—22no—
75C8—81no—
76C2×C3—21no—
77C2×C3—81no—
78C2×C3#35311yescharacteristic
79C22—41no—
80C22—81no—
81C22C3×#9911yescharacteristic
82C4—21no—
83C4—41no—
84C4—41no—
85C4—81no—
86C4—161no—
87C3#140711yescharacteristic, direct product factor, Sylow
88C2—21no—
89C2—81no—
90C2C3×#35311yescharacteristic
subgroupG/H
center, socleC2×C3#353
commutatorC42C2×C3×C4
Frattini, cosocle#124C22×C3
prime radicalC2×C3×D4D4
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#124 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1407C3direct (N × H)
7. C3×C4⋊Q8C4semidirect
11. C3×#97C4semidirect
28. C4⋊Q8C3×C4semidirect
32. #97C3×C4semidirect
87. C3#1407direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#4972
C3×#3552
C3×#3542
#14073