Finite Group Databasebeta

← C3⋊(#1842⋊C3) #11920156

Subgroups — C3⋊(#1842⋊C3) #11920156

Order 1152.

149 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 149 conjugacy classes of subgroups — too many to draw. Only its 27 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×C4×C42⋊C3C211yesmaximal, characteristic
2#69394C311yesmaximal, characteristic, complemented
3#1842⋊C3—31nomaximal
4C2×C3×C42⋊C3C411yescharacteristic
5A4×C3⋊C8—41nomaximal
6C3×C43C2×C311yescharacteristic
7C2×C4⋊(C3⋊C8)—31no—
8C2×C4⋊(C3⋊C8)—31no—
9C4×C42⋊C3—21no—
10C4×C42⋊C3D311yescharacteristic
11C3×C4×A4—41no—
12C3×C42⋊C3C811yescharacteristic, complemented
13#1842—31noSylow
14C2×C3×C42—31no—
15C2×C3×C42—31no—
16C2×C3×C42C3×C411yescharacteristic
17C22×C3⋊C8—31no—
18C22×C3⋊C8A411yescharacteristic
19C8×A4—121no—
20C2×C42⋊C3—21no—
21C2×C42⋊C3Dic311yescharacteristic
22C4⋊(C3⋊C8)—62no—
23C4⋊(C3⋊C8)—62no—
24C2×C3×A4—41no—
25C3×C3⋊C8—161no—
26C2×C4⋊C8—91no—
27C2×C4⋊C8—91no—
28C43C3×D311yescharacteristic
29C22×C3×C4—31no—
30C22×C3×C4—31no—
31C22×C3×C4C2×A411yescharacteristic
32C4×A4—41no—
33C4×A4—81no—
34C3×C42—31no—
35C3×C42—32no—
36C3×C42—32no—
37C3×C42—62no—
38C3×C42C3×C811yescharacteristic, complemented
39C2×C3⋊C8—61no—
40C2×C3⋊C8—61no—
41C2×C3⋊C8—62no—
42C42⋊C3—21no—
43C42⋊C3C3⋊C811yescharacteristic, complemented
44C3×A4—41no—
45C32×C4—161no—
46C22×C8—31no—
47C22×C8—91no—
48C2×C42—31no—
49C2×C42—31no—
50C2×C42C3×Dic311yescharacteristic
51C4⋊C8—182no—
52C4⋊C8—182no—
53C23×C3C4×A411yescharacteristic
54C2×A4—41no—
55C2×A4—81no—
56C2×C3×C4—32no—
57C2×C3×C4—32no—
58C2×C3×C4—31no—
59C2×C3×C4—31no—
60C2×C3×C4—31no—
61C2×C3×C4—31no—
62C2×C3×C4—32no—
63C2×C3×C4—62no—
64C3×C8—481no—
65C3⋊C8—41no—
66C3⋊C8—121no—
67C2×C32—161no—
68C22×C4—31no—
69C22×C4—31no—
70C22×C4D3×A411yescharacteristic
71C2×C8—181no—
72C2×C8—181no—
73C2×C8—182no—
74C42—31no—
75C42—32no—
76C42—32no—
77C42—62no—
78C42C3×C3⋊C811yescharacteristic, complemented
79C22×C3—31no—
80C22×C3—31no—
81C22×C3C8×A411yescharacteristic
82A4—41no—
83A4—81no—
84C3×C4—32no—
85C3×C4—32no—
86C3×C4—31no—
87C3×C4—62no—
88C3×C4—161no—
89C3×C4—321no—
90C3×C4#127⋊C311yescharacteristic
91C32—161noSylow
92C23Dic3×A411yescharacteristic
93C2×C4—32no—
94C2×C4—32no—
95C2×C4—31no—
96C2×C4—31no—
97C2×C4—31no—
98C2×C4—31no—
99C2×C4—32no—
100C2×C4—62no—
101C8—121no—
102C8—361no—
103C2×C3—31no—
104C2×C3—31no—
105C2×C3—161no—
106C2×C3—321no—
107C2×C3#384⋊C311yescharacteristic
108C22—31no—
109C22—31no—
110C22A4×C3⋊C811yescharacteristic
111C4—32no—
112C4—32no—
113C4—31no—
114C4—62no—
115C4C3⋊(#127⋊C3)11yescharacteristic
116C3—161no—
117C3—321no—
118C3#1842⋊C311yescharacteristic, complemented
119C2—31no—
120C2—31no—
121C2C3⋊(#384⋊C3)11yescharacteristic
subgroupG/H
center, hypercenterC4C3⋊(#127⋊C3)
commutator, hypocenterC3×C42C3×C8
FrattiniC22×C4D3×A4
Fitting, cosocleC3×C43C2×C3
socleC23×C3C4×A4
prime radicalC2×C3×C42⋊C3C4
LCSG ▷ C3×C42
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. #69394C3semidirect
12. C3×C42⋊C3C8semidirect
38. C3×C42C3×C8semidirect
43. C42⋊C3C3⋊C8semidirect
78. C42C3×C3⋊C8semidirect
118. C3#1842⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×C4×C42⋊C32
#693943
#1842⋊C33
A4×C3⋊C84