Finite Group Databasebeta

← #14518693

Subgroups — #14518693

Order 1944.

466 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 81 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⋊(C3⋊(3−1+2⋊C4))C211yesmaximal, characteristic
23−1+2×C3⋊Dic3C211yesmaximal, characteristic
3C32×3−1+2⋊C4C211yesmaximal, characteristic
4C3×#6293—31nomaximal
5#10619867C311yesmaximal, characteristic, complemented
6#6189⋊C3—34nomaximal
7C2×C32×3−1+2C2211yescharacteristic
8C3×C3⋊(C3⋊Dic3)—31no—
9C32×C3⋊Dic3D311yescharacteristic
10C33×Dic3—31no—
11C3⋊(C3⋊Dic9)C2×C311yescharacteristic
12C3⋊(3−1+2⋊C4)—34no—
13C3⋊(3−1+2⋊C4)—64no—
14C9×C3⋊Dic3—21no—
15C9×C3⋊Dic3C2×C311yescharacteristic
16Dic3×3−1+2—34no—
17C3×3−1+2⋊C4—24no—
18C3×3−1+2⋊C4D314yes—
19C32×Dic9C2×C311yescharacteristic
20C32×3−1+2Q811yescharacteristic, complemented, Sylow
21C3×#634—91no—
22#6293—31no—
23C3×#627—94no—
243−1+2⋊Q8—91no—
25#6189—34no—
26C2×C34C2×D311yescharacteristic
27C2×C3×3−1+2—24no—
28C2×C3×3−1+2—24no—
29C2×C3×3−1+2—44no—
30C2×C3×3−1+2C2×D314yes—
31C2×C32×C9—21no—
32C2×C32×C9C22×C311yescharacteristic
33C33×C4—91no—
34C3⋊(C3⋊Dic3)—31no—
35C3×C3⋊Dic3—31no—
36C3×C3⋊Dic3—91no—
37C3×C3⋊Dic3—94no—
38C3×C3⋊Dic3—184no—
39C3×C3⋊Dic3C3×D311yescharacteristic
40C32×Dic3—34no—
41C32×Dic3—34no—
42C32×Dic3—31no—
43C32×Dic3—64no—
44C4×3−1+2—91no—
45C3⋊Dic9—34no—
46C3⋊Dic9—64no—
473−1+2⋊C4—24no—
483−1+2⋊C4—91no—
493−1+2⋊C4—184no—
503−1+2⋊C4C3⋊D311yescharacteristic
51C9×Dic3—34no—
52C9×Dic3—64no—
53C3×Dic9C3×D314yes—
54C34Dic611yescharacteristic
55C3×3−1+2—24no—
56C3×3−1+2—24no—
57C3×3−1+2—44no—
58C3×3−1+2Dic614yescomplemented
59C32×C9—21no—
60C32×C9C3×Q811yescharacteristic, complemented
61#634—91no—
62C3×Dic6—271no—
63C3×Dic6—274no—
64#627—94no—
65Dic18—91no—
66C2×C33—24no—
67C2×C33—31no—
68C2×C33—64no—
69C2×C33D3214yes—
70C2×C33C2×C3×D311yescharacteristic
71C2×3−1+2—24no—
72C2×3−1+2—24no—
73C2×3−1+2—44no—
74C2×3−1+2—412no—
75C2×3−1+2C2×C3⋊D311yescharacteristic
76C2×C3×C9—24no—
77C2×C3×C9—24no—
78C2×C3×C9—44no—
79C2×C3×C9C2×C3×D314yes—
80C32×C4—91no—
81C32×C4—94no—
82C32×C4—91no—
83C32×C4—184no—
84C3⋊Dic3—91no—
85C3⋊Dic3—94no—
86C3⋊Dic3—184no—
87C3⋊Dic3AGL(1,ℤ/9)11yescharacteristic
88C3×Dic3—34no—
89C3×Dic3—34no—
90C3×Dic3—31no—
91C3×Dic3—64no—
92C3×Dic3—94no—
93C3×Dic3—274no—
94C3×Dic3—271no—
95C3×Dic3—544no—
96C4×C9—91no—
97C4×C9—181no—
98Dic9—91no—
99Dic9—184no—
100Dic9C3×C3⋊D311yescharacteristic
101C33—24no—
102C33—31no—
103C33—64no—
104C33#62714yes—
105C33C3×Dic611yescharacteristic
1063−1+2—24no—
1073−1+2—24no—
1083−1+2—44no—
1093−1+2—412no—
1103−1+2#63411yescharacteristic, complemented
111C3×C9—24no—
112C3×C9—24no—
113C3×C9—44no—
114C3×C9C3×Dic614yescomplemented
115C3×Q8—811no—
116Dic6—271no—
117Dic6—274no—
118C2×C32—24no—
119C2×C32—24no—
120C2×C32—34no—
121C2×C32—64no—
122C2×C32—64no—
123C2×C32—124no—
124C2×C32C2×AGL(1,ℤ/9)11yescharacteristic
125C2×C32C3×D3214yes—
126C2×C32D3×C3⋊D311yescharacteristic
127C2×C9—21no—
128C2×C9—24no—
129C2×C9—44no—
130C2×C9C2×C3×C3⋊D311yescharacteristic
131C3×C4—91no—
132C3×C4—94no—
133C3×C4—91no—
134C3×C4—184no—
135C3×C4—271no—
136C3×C4—811no—
137Dic3—34no—
138Dic3—31no—
139Dic3—274no—
140Dic3—271no—
141Dic3—544no—
142C32—24no—
143C32—24no—
144C32—34no—
145C32—64no—
146C32—64no—
147C32—124no—
148C323−1+2⋊Q811yescharacteristic, complemented
149C32C3×#62714yes—
150C32#629311yescharacteristic
151C9—21no—
152C9—24no—
153C9—44no—
154C9C3×#63411yescharacteristic, complemented
155Q8—811noSylow
156C2×C3—24no—
157C2×C3—31no—
158C2×C3—64no—
159C2×C3D3×AGL(1,ℤ/9)14yes—
160C2×C3C3×D3×C3⋊D311yescharacteristic
161C4—91no—
162C4—91no—
163C4—811no—
164C3—24no—
165C3—31no—
166C3—64no—
167C3#6189⋊C314yescomplemented
168C3C3×#629311yescharacteristic
169C2C3⋊D3×AGL(1,ℤ/9)11yescharacteristic
subgroupG/H
center, hypercenterC2C3⋊D3×AGL(1,ℤ/9)
commutator, cosocleC2×C32×C9C22×C3
FrattiniC2×C3C3×D3×C3⋊D3
FittingC2×C32×3−1+2C22
socleC2×C33C2×C3×D3
prime radicalC2×C34C2×D3
hypocenterC32×C9C3×Q8
LCSG ▷ C2×C32×C9 ▷ C32×C9
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
5. #10619867C3semidirect
20. C32×3−1+2Q8semidirect
58. C3×3−1+2Dic6semidirect
60. C32×C9C3×Q8semidirect
110. 3−1+2#634semidirect
114. C3×C9C3×Dic6semidirect
148. C323−1+2⋊Q8semidirect
154. C9C3×#634semidirect
167. C3#6189⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C3⋊(3−1+2⋊C4))2
3−1+2×C3⋊Dic32
C32×3−1+2⋊C42
C3×#62933
#106198673
#6189⋊C33