Finite Group Databasebeta

← C3⋊D3×#103 #10592500

Subgroups — C3⋊D3×#103 #10592500

Order 576.

486 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 119 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
1C2×Q8×C3⋊D3C211yesmaximal, characteristic
2C2×C8×C3⋊D3C211yesmaximal, characteristic
3C4⋊C4×C3⋊D3C211yesmaximal, characteristic
4C32×#103C211yesmaximal, characteristic, complemented
5#63662C211yesmaximal, characteristic, complemented
6#63643C211yesmaximal, characteristic, complemented
7#63637C211yesmaximal, characteristic, complemented
8D3×#103—34nomaximal
9C2×C32×Q8C2211yescharacteristic
10Q8×C3⋊D3—22no—
11Q8×C3⋊D3C414yescomplemented
12C2×C4×C3⋊D3—21no—
13C2×C4×C3⋊D3—21no—
14C2×C4×C3⋊D3C2211yescharacteristic
15C2×#634—21no—
16C2×#634C2211yescharacteristic
17C2×C32×C8C2211yescharacteristic
18C32×C4⋊C4C2211yescharacteristic
19C4⋊(C3⋊Dic3)C2211yescharacteristic
20#3750—21no—
21C2×C3⋊(C3⋊C8)C2211yescharacteristic
22C8×C3⋊D3—22no—
23C2×D3×Q8—34no—
24C2×D3×C8—34no—
25D3×C4⋊C4—34no—
26C3×#103D314yescomplemented
27#835—34no—
28#816—34no—
29#810—34no—
30C22×C3⋊D3D411yescharacteristic
31C32×Q8—21no—
32C32×Q8C2×C412yescomplemented
33C2×C32×C4—21no—
34C2×C32×C4—21no—
35C2×C32×C4C2311yescharacteristic
36C2×C3⋊Dic3—21no—
37C2×C3⋊Dic3—21no—
38C2×C3⋊Dic3D411yescharacteristic
39C4×C3⋊D3—24no—
40C4×C3⋊D3—42no—
41C4×C3⋊D3C2×C412yes—
42C4×C3⋊D3D412yes—
43#634—21no—
44#634—24no—
45#634C2×C412yescomplemented
46C32×C8—21no—
47C3⋊(C3⋊C8)—21no—
48C2×#103—91noSylow
49C2×C3×Q8C2×D314yes—
50D3×Q8—316no—
51D3×Q8—68no—
52C2×C4×D3—34no—
53C2×C4×D3—64no—
54C2×C4×D3—64no—
55C2×Dic6—34no—
56C2×Dic6—64no—
57C2×C3×C8C2×D314yes—
58C3×C4⋊C4C2×D314yes—
59C4⋊Dic3—34no—
60Dic3⋊C4—64no—
61C2×C3⋊C8—34no—
62D3×C8—68no—
63C22×C32C2×D411yescharacteristic
64C2×C3⋊D3C22⋊C412yes—
65C2×C3⋊D3SD1612yes—
66C2×C3⋊D3Q1612yes—
67C32×C4—22no—
68C32×C4—41no—
69C32×C4C22×C411yescharacteristic
70C32×C4C2×D411yescharacteristic
71C3⋊Dic3—22no—
72C3⋊Dic3—41no—
73C3⋊Dic3C22⋊C412yes—
74C22×Q8—91no—
75C22×C8—91no—
76C2×C4⋊C4—91no—
77#103—91no—
78#103—91no—
79#103—91no—
80#103C3⋊D311yescharacteristic, direct product factor
81C22×D3—34no—
82C3×Q8—24no—
83C3×Q8C4×D318yescomplemented
84C2×C3×C4—24no—
85C2×C3×C4—24no—
86C2×C3×C4C22×D314yes—
87C2×Dic3—34no—
88C2×Dic3—64no—
89C2×Dic3—64no—
90C4×D3—38no—
91C4×D3—38no—
92C4×D3—616no—
93C4×D3—128no—
94Dic6—38no—
95Dic6—616no—
96Dic6—64no—
97C3×C8—24no—
98C3⋊C8—64no—
99C2×C32C2×C22⋊C411yescharacteristic
100C2×C32C2×SD1611yescharacteristic
101C2×C32C2×Q1611yescharacteristic
102C3⋊D3#10314yesdirect product factor
103C2×Q8—94no—
104C2×Q8—91no—
105C2×Q8—181no—
106C2×Q8—182no—
107C2×Q8C2×C3⋊D311yescharacteristic
108C22×C4—91no—
109C22×C4—181no—
110C22×C4—181no—
111C2×C8—91no—
112C2×C8—182no—
113C2×C8C2×C3⋊D311yescharacteristic
114C4⋊C4—91no—
115C4⋊C4—181no—
116C4⋊C4C2×C3⋊D311yescharacteristic
117C22×C3D3×D414yes—
118C2×D3—38no—
119C2×D3—38no—
120C2×D3—38no—
121C3×C4—28no—
122C3×C4—44no—
123C3×C4C2×C4×D314yes—
124C3×C4D3×D414yes—
125Dic3—38no—
126Dic3—68no—
127Dic3—124no—
128C32C2×#10311yescharacteristic, complemented, Sylow
129C23—91no—
130Q8—21no—
131Q8—92no—
132Q8—184no—
133Q8—181no—
134Q8C4×C3⋊D312yescomplemented
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—91no—
138C2×C4—92no—
139C2×C4—92no—
140C2×C4—184no—
141C2×C4—181no—
142C2×C4—181no—
143C2×C4—362no—
144C2×C4C22×C3⋊D311yescharacteristic
145C8—21no—
146C8—181no—
147C2×C3D3×C22⋊C414yes—
148C2×C3D3×SD1614yes—
149C2×C3D3×Q1614yes—
150D3—316no—
151C22—92no—
152C22—92no—
153C22—92no—
154C22D4×C3⋊D311yescharacteristic
155C4—22no—
156C4—41no—
157C4—92no—
158C4—182no—
159C4—361no—
160C4C2×C4×C3⋊D311yescharacteristic
161C4D4×C3⋊D311yescharacteristic
162C3D3×#10314yescomplemented
163C2—94no—
164C2C22⋊C4×C3⋊D311yescharacteristic
165C2SD16×C3⋊D311yescharacteristic
166C2Q16×C3⋊D311yescharacteristic
subgroupG/H
centerC22D4×C3⋊D3
commutatorC32×C4C22×C4
FrattiniC2×C4C22×C3⋊D3
FittingC32×#103C2
socleC22×C32C2×D4
prime radicalC22×C3⋊D3D4
cosocleC2×C32×C4C23
hypercenter#103C3⋊D3
hypocenterC32C2×#103
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
4. C32×#103C2semidirect
5. #63662C2semidirect
6. #63643C2semidirect
7. #63637C2semidirect
11. Q8×C3⋊D3C4semidirect
26. C3×#103D3semidirect
32. C32×Q8C2×C4semidirect
45. #634C2×C4semidirect
80. #103C3⋊D3direct (N × H)
83. C3×Q8C4×D3semidirect
102. C3⋊D3#103direct (N × H)
128. C32C2×#103semidirect
134. Q8C4×C3⋊D3semidirect
162. C3D3×#103semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊D32
C2×C8×C3⋊D32
C4⋊C4×C3⋊D32
C32×#1032
#636622
#636432
#636372
D3×#1033