Finite Group Databasebeta

← C3⋊#1304 #67623

Subgroups — C3⋊#1304 #67623

Order 384.

396 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 65 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×#379C211yesmaximal, characteristic
2#5247C212yesmaximal
3#1304—31nomaximal, Sylow
4C25×C3C2211yescharacteristic
5C2×C3×C22⋊C4—22no—
6C2×C3×C22⋊C4C412yescomplemented
7C2×#217—22no—
8C2×#217—22no—
9C2×#217C414yescomplemented
10#379—32no—
11#379D311yescharacteristic
12C24×C3—44no—
13C24×C3—42no—
14C24×C3C2×C412yes—
15C24×C3C2×C411yescharacteristic
16C24×C3D411yescharacteristic
17C24×C3D412yes—
18C24×C3Q811yescharacteristic
19C22×C3×C4—22no—
20C22×Dic3—24no—
21C3×C22⋊C4—44no—
22C3×C22⋊C4—42no—
23#217—44no—
24#217—44no—
25#217—44no—
26C25C2×D311yescharacteristic
27C2×C22⋊C4—22no—
28C2×C22⋊C4—34no—
29C2×C22⋊C4—62no—
30C2×C22⋊C4—62no—
31C2×C22⋊C4Dic312yescomplemented
32C23×C3—24no—
33C23×C3—24no—
34C23×C3—24no—
35C23×C3—22no—
36C23×C3—24no—
37C23×C3—42no—
38C23×C3—42no—
39C23×C3—42no—
40C23×C3—41no—
41C23×C3—42no—
42C23×C3—41no—
43C23×C3—42no—
44C23×C3—416no—
45C23×C3C4211yescharacteristic
46C23×C3C22⋊C412yes—
47C23×C3C22⋊C411yescharacteristic
48C23×C3C4⋊C412yes—
49C23×C3C4⋊C411yescharacteristic
50C2×C3×C4—44no—
51C2×C3×C4—42no—
52C2×Dic3—44no—
53C2×Dic3—44no—
54C2×Dic3—44no—
55C24—44no—
56C24—42no—
57C24Dic611yescharacteristic
58C24C4×D312yes—
59C24D1211yescharacteristic
60C24C2×Dic311yescharacteristic
61C24#6712yes—
62C22×C4—22no—
63C22×C4—64no—
64C22⋊C4—44no—
65C22⋊C4—42no—
66C22⋊C4—124no—
67C22⋊C4—124no—
68C22⋊C4—124no—
69C22×C3—22no—
70C22×C3—22no—
71C22×C3—22no—
72C22×C3—21no—
73C22×C3—22no—
74C22×C3—22no—
75C22×C3—21no—
76C22×C3—22no—
77C22×C3—22no—
78C22×C3—22no—
79C22×C3—44no—
80C22×C3—48no—
81C22×C3—48no—
82C22×C3—44no—
83C22×C3—44no—
84C22×C3#9511yescharacteristic
85C22×C3#9914yes—
86C22×C3#9912yes—
87C3×C4—82no—
88Dic3—84no—
89C23—24no—
90C23—24no—
91C23—24no—
92C23—22no—
93C23—24no—
94C23—41no—
95C23—42no—
96C23—42no—
97C23—42no—
98C23—41no—
99C23—42no—
100C23—42no—
101C23—416no—
102C23C4×Dic311yescharacteristic
103C23Dic3⋊C412yes—
104C23C4⋊Dic311yescharacteristic
105C23(C2×D3)⋊C412yes—
106C23#21711yescharacteristic
107C2×C4—44no—
108C2×C4—42no—
109C2×C4—124no—
110C2×C4—124no—
111C2×C4—124no—
112C2×C3—24no—
113C2×C3—22no—
114C2×C3—41no—
115C2×C3—42no—
116C2×C3—41no—
117C2×C3#34211yescharacteristic
118C2×C3#34212yes—
119C22—22no—
120C22—22no—
121C22—22no—
122C22—21no—
123C22—22no—
124C22—21no—
125C22—22no—
126C22—22no—
127C22—22no—
128C22—22no—
129C22—48no—
130C22—44no—
131C22—44no—
132C22—48no—
133C22—44no—
134C22#80614yes—
135C22C3⋊#9511yescharacteristic
136C22#83412yes—
137C4—82no—
138C4—244no—
139C3#130411yescharacteristic, complemented, Sylow
140C2—22no—
141C2—24no—
142C2—41no—
143C2—42no—
144C2—41no—
145C2#452611yescharacteristic
146C2#452712yes—
subgroupG/H
centerC22C3⋊#95
commutatorC23×C3C42
FrattiniC25C2×D3
FittingC3×#379C2
socleC22×C3#95
prime radical, cosocleC25×C3C22
hypercenter#379D3
hypocenterC3#1304
LCSG ▷ C23×C3 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C25 ◁ #379

Complements

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

NH ≅ G/Ntype
6. C2×C3×C22⋊C4C4semidirect
9. C2×#217C4semidirect
31. C2×C22⋊C4Dic3semidirect
139. C3#1304semidirect

Maximal subgroups

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

subgroupindex
C3×#3792
#52472
#13043