Finite Group Databasebeta

← C3×#1346 #67906

Subgroups — C3×#1346 #67906

Order 384.

124 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 40 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×#398C211yesmaximal, characteristic
2C3×#343C211yesmaximal, characteristic
3C3×#324C211yesmaximal, characteristic
4#1346C311yesmaximal, characteristic, direct product factor, Sylow
5C2×C3×M16—21no—
6C2×C3×C4⋊C4—21no—
7C2×C3×C4⋊C4C411yescharacteristic
8C2×C3×C4⋊C4C2211yescharacteristic
9C3×C22⋊C8—21no—
10C3×#95—21no—
11C3×#95C411yescharacteristic
12#398C2×C311yescharacteristic
13#343C2×C311yescharacteristic
14#324C2×C311yescharacteristic
15C22×C3×C4—21no—
16C22×C3×C4—21no—
17C22×C3×C4C2×C411yescharacteristic
18C22×C3×C4D411yescharacteristic
19C22×C3×C4D411yescharacteristic
20C3×M16—22no—
21C3×M16—41no—
22C2×C3×C8—41no—
23C2×C3×C8—41no—
24C3×C4⋊C4—41no—
25C3×C4⋊C4—41no—
26C3×C4⋊C4—41no—
27C3×C4⋊C4—41no—
28C2×M16—21no—
29C2×C4⋊C4—21no—
30C2×C4⋊C4C3×C411yescharacteristic
31C2×C4⋊C4C22×C311yescharacteristic
32C22⋊C8—21no—
33#95—21no—
34#95C3×C411yescharacteristic
35C23×C3C22⋊C411yescharacteristic
36C2×C3×C4—21no—
37C2×C3×C4—21no—
38C2×C3×C4—22no—
39C2×C3×C4—21no—
40C2×C3×C4—21no—
41C2×C3×C4—41no—
42C2×C3×C4—41no—
43C2×C3×C4—41no—
44C2×C3×C4—41no—
45C2×C3×C4—41no—
46C2×C3×C4—41no—
47C2×C3×C4—41no—
48C2×C3×C4D811yescharacteristic
49C2×C3×C4SD1611yescharacteristic
50C3×C8—42no—
51C3×C8—81no—
52C22×C4—21no—
53C22×C4—21no—
54C22×C4C2×C3×C411yescharacteristic
55C22×C4C3×D411yescharacteristic
56C22×C4C3×D411yescharacteristic
57M16—22no—
58M16—41no—
59C2×C8—41no—
60C2×C8—41no—
61C4⋊C4—41no—
62C4⋊C4—41no—
63C4⋊C4—41no—
64C4⋊C4—41no—
65C22×C3—21no—
66C22×C3—21no—
67C22×C3#9911yescharacteristic
68C22×C3#10211yescharacteristic
69C22×C3#10411yescharacteristic
70C3×C4—21no—
71C3×C4—21no—
72C3×C4—42no—
73C3×C4—41no—
74C3×C4—41no—
75C3×C4—81no—
76C23C3×C22⋊C411yescharacteristic
77C2×C4—21no—
78C2×C4—21no—
79C2×C4—22no—
80C2×C4—21no—
81C2×C4—21no—
82C2×C4—41no—
83C2×C4—41no—
84C2×C4—41no—
85C2×C4—41no—
86C2×C4—41no—
87C2×C4—41no—
88C2×C4—41no—
89C2×C4C3×D811yescharacteristic
90C2×C4C3×SD1611yescharacteristic
91C8—42no—
92C8—81no—
93C2×C3—21no—
94C2×C3—21no—
95C2×C3#32711yescharacteristic
96C2×C3#35211yescharacteristic
97C2×C3#35611yescharacteristic
98C22—21no—
99C22—21no—
100C22C3×#9911yescharacteristic
101C22C3×#10211yescharacteristic
102C22C3×#10411yescharacteristic
103C4—21no—
104C4—21no—
105C4—42no—
106C4—41no—
107C4—41no—
108C4—81no—
109C3#134611yescharacteristic, direct product factor, Sylow
110C2—21no—
111C2—21no—
112C2C3×#32711yescharacteristic
113C2C3×#35211yescharacteristic
114C2C3×#35611yescharacteristic
subgroupG/H
center, socleC22×C3#99
commutatorC22×C4C2×C3×C4
Frattini, cosocleC2×C4⋊C4C22×C3
prime radicalC23×C3C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C2×C3×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1346C3direct (N × H)
109. C3#1346direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#3982
C3×#3432
C3×#3242
#13463