Finite Group Databasebeta

← C3×#1354 #67914

Subgroups — C3×#1354 #67914

Order 384.

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

normal subgroups only

This group has 140 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×#395C211yesmaximal, characteristic
2C3×#343C211yesmaximal, characteristic
3C3×#324C211yesmaximal, characteristic
4#1354C311yesmaximal, characteristic, direct product factor, Sylow
5C22×C3×Q8C411yescharacteristic
6C2×C3×M16—21no—
7C2×C3×C4⋊C4—21no—
8C2×C3×C4⋊C4C2211yescharacteristic
9C3×C22⋊C8—21no—
10C3×#95—21no—
11C3×#95C411yescharacteristic
12#395C2×C311yescharacteristic
13#343C2×C311yescharacteristic
14#324C2×C311yescharacteristic
15C2×C3×Q8—42no—
16C2×C3×Q8—41no—
17C22×C3×C4—21no—
18C22×C3×C4—21no—
19C22×C3×C4C2×C411yescharacteristic
20C22×C3×C4D411yescharacteristic
21C22×C3×C4D411yescharacteristic
22C3×M16—22no—
23C3×M16—41no—
24C2×C3×C8—41no—
25C2×C3×C8—41no—
26C3×C4⋊C4—41no—
27C3×C4⋊C4—42no—
28C22×Q8C3×C411yescharacteristic
29C2×M16—21no—
30C2×C4⋊C4—21no—
31C2×C4⋊C4C22×C311yescharacteristic
32C22⋊C8—21no—
33#95—21no—
34#95C3×C411yescharacteristic
35C23×C3C22⋊C411yescharacteristic
36C3×Q8—42no—
37C3×Q8—42no—
38C2×C3×C4—21no—
39C2×C3×C4—21no—
40C2×C3×C4—22no—
41C2×C3×C4—22no—
42C2×C3×C4—21no—
43C2×C3×C4—21no—
44C2×C3×C4—41no—
45C2×C3×C4—41no—
46C2×C3×C4—41no—
47C2×C3×C4—41no—
48C2×C3×C4—41no—
49C2×C3×C4—41no—
50C2×C3×C4SD1611yescharacteristic
51C2×C3×C4Q1611yescharacteristic
52C3×C8—42no—
53C3×C8—81no—
54C2×Q8—42no—
55C2×Q8—41no—
56C22×C4—21no—
57C22×C4—21no—
58C22×C4C2×C3×C411yescharacteristic
59C22×C4C3×D411yescharacteristic
60C22×C4C3×D411yescharacteristic
61M16—22no—
62M16—41no—
63C2×C8—41no—
64C2×C8—41no—
65C4⋊C4—41no—
66C4⋊C4—42no—
67C22×C3—21no—
68C22×C3—21no—
69C22×C3#9911yescharacteristic
70C22×C3#10311yescharacteristic
71C22×C3#10411yescharacteristic
72C3×C4—21no—
73C3×C4—21no—
74C3×C4—42no—
75C3×C4—41no—
76C3×C4—42no—
77C3×C4—41no—
78C23C3×C22⋊C411yescharacteristic
79Q8—42no—
80Q8—42no—
81C2×C4—21no—
82C2×C4—21no—
83C2×C4—22no—
84C2×C4—22no—
85C2×C4—21no—
86C2×C4—21no—
87C2×C4—41no—
88C2×C4—41no—
89C2×C4—41no—
90C2×C4—41no—
91C2×C4—41no—
92C2×C4—41no—
93C2×C4C3×SD1611yescharacteristic
94C2×C4C3×Q1611yescharacteristic
95C8—42no—
96C8—81no—
97C2×C3—21no—
98C2×C3—21no—
99C2×C3#32811yescharacteristic
100C2×C3AΣL(1,𝔽16)11yescharacteristic
101C2×C3#35611yescharacteristic
102C22—21no—
103C22—21no—
104C22C3×#9911yescharacteristic
105C22C3×#10311yescharacteristic
106C22C3×#10411yescharacteristic
107C4—21no—
108C4—21no—
109C4—42no—
110C4—41no—
111C4—42no—
112C4—41no—
113C3#135411yescharacteristic, direct product factor, Sylow
114C2—21no—
115C2—21no—
116C2C3×#32811yescharacteristic
117C2C3×AΣL(1,𝔽16)11yescharacteristic
118C2C3×#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. #1354C3direct (N × H)
113. C3#1354direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#3952
C3×#3432
C3×#3242
#13543