Finite Group Databasebeta

← #14518789

Subgroups — #14518789

Order 1944.

1320 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 140 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×C3⋊(C3⋊(C3⋊D9))C211yesmaximal, characteristic
2C3×C9×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C32×C3⋊Dic9C211yesmaximal, characteristic, complemented
4#10620150—31nomaximal
5#10619872—34nomaximal
6#10619870—33nomaximal
7C2×C33×C9C2211yescharacteristic
8C3⋊(C3⋊(C3⋊D9))C412yescomplemented
9C2×C3⋊(C3⋊(C3⋊D3))—31no—
10C32×C3⋊Dic3—31no—
11C32×C3⋊Dic3D311yescharacteristic
12C2×C3⋊(C3⋊D9)—33no—
13C2×C3⋊(C3⋊D9)—34no—
14C2×C3⋊(C3⋊D9)—612no—
15C2×C3⋊(C3⋊D9)—64no—
16C9×C3⋊Dic3D313yescomplemented
17C3×C3⋊Dic9D314yescomplemented
18C3×C9×Dic3—34no—
19C32×Dic9—33no—
20C33×C9C2×C411yescharacteristic, complemented, Sylow
21#6289—94no—
22#6289—93no—
23#6289—91no—
24C4×C3⋊D9—91no—
25(C3⋊D9)⋊C4—912no—
26C2×C34C2×D311yescharacteristic
27C3⋊(C3⋊(C3⋊D3))—32no—
28C2×C32×C9—24no—
29C2×C32×C9—212no—
30C2×C32×C9C2×D313yes—
31C2×C32×C9C2×D314yes—
32C3⋊(C3⋊D9)—38no—
33C3⋊(C3⋊D9)—36no—
34C3⋊(C3⋊D9)—624no—
35C3⋊(C3⋊D9)—68no—
36C2×C3⋊(C3⋊D3)—93no—
37C2×C3⋊(C3⋊D3)—94no—
38C2×C3⋊(C3⋊D3)—91no—
39C2×C3⋊(C3⋊D3)—184no—
40C2×C3⋊(C3⋊D3)—1812no—
41C3×C3⋊Dic3—34no—
42C3×C3⋊Dic3D913yescomplemented
43C3×C3⋊Dic3C3⋊D311yescharacteristic
44C32×Dic3—34no—
45C32×Dic3—93no—
46C32×Dic3—91no—
47C2×C3⋊D9—912no—
48C2×C3⋊D9—91no—
49C2×C3⋊D9—1812no—
50C2×C3⋊D9—184no—
51C2×C3⋊D9—1812no—
52C2×C3⋊D9—1824no—
53C3×C4×C9—91no—
54C3⋊Dic9C3⋊D311yescharacteristic, complemented
55C9×Dic3—312no—
56C3×Dic9—312no—
57C34C4×D311yescharacteristic
58C32×C9—24no—
59C32×C9—212no—
60C32×C9C4×D313yescomplemented
61C32×C9C4×D314yescomplemented
62C4×C3⋊D3—271no—
63C4×C3⋊D3—271no—
64#624—274no—
65#624—2712no—
66C4×D9—273no—
67C2×C33—212no—
68C2×C33—24no—
69C2×C33C2×D913yes—
70C2×C33D3214yes—
71C2×C33C2×C3⋊D311yescharacteristic
72C3⋊(C3⋊D3)—96no—
73C3⋊(C3⋊D3)—98no—
74C3⋊(C3⋊D3)—92no—
75C3⋊(C3⋊D3)—188no—
76C3⋊(C3⋊D3)—1824no—
77C2×C3×C9—224no—
78C2×C3×C9—212no—
79C2×C3×C9—24no—
80C2×C3×C9—212no—
81C2×C3×C9D32112yes—
82C2×C3×C9C2×C3⋊D311yescharacteristic
83C3⋊D9—92no—
84C3⋊D9—924no—
85C3⋊D9—1824no—
86C3⋊D9—188no—
87C3⋊D9—1824no—
88C3⋊D9—1848no—
89C2×C3⋊D3—271no—
90C2×C3⋊D3—271no—
91C2×C3⋊D3—2712no—
92C2×C3⋊D3—274no—
93C2×C3⋊D3—544no—
94C2×C3⋊D3—5412no—
95C2×C3⋊D3—5412no—
96C2×C3⋊D3—544no—
97C2×C3⋊D3—5424no—
98C32×C4—91no—
99C32×C4—271no—
100C3⋊Dic3—31no—
101C3⋊Dic3C3⋊D911yescharacteristic, complemented
102C3×Dic3—312no—
103C3×Dic3—34no—
104C3×Dic3—912no—
105C3×Dic3—94no—
106C2×D9—273no—
107C2×D9—5412no—
108C4×C9—93no—
109Dic9—33no—
110C33—212no—
111C33—24no—
112C33C4×D913yescomplemented
113C33#62414yes—
114C33C4×C3⋊D311yescharacteristic
115C3×C9—224no—
116C3×C9—212no—
117C3×C9—24no—
118C3×C9—212no—
119C3×C9#624112yescomplemented
120C3×C9C4×C3⋊D311yescharacteristic, complemented
121C4×D3—814no—
122C4×D3—811no—
123C4×D3—813no—
124C2×C32—224no—
125C2×C32—212no—
126C2×C32—212no—
127C2×C32—24no—
128C2×C32—24no—
129C2×C32D3×D9112yes—
130C2×C32C2×C3⋊D911yescharacteristic
131C2×C32D3×C3⋊D314yes—
132C2×C32D3×C3⋊D311yescharacteristic
133C3⋊D3—272no—
134C3⋊D3—272no—
135C3⋊D3—2724no—
136C3⋊D3—278no—
137C3⋊D3—548no—
138C3⋊D3—5424no—
139C3⋊D3—5424no—
140C3⋊D3—548no—
141C3⋊D3—5448no—
142C2×C9—212no—
143C2×C9D3×C3⋊D313yes—
144D9—276no—
145D9—5424no—
146C2×D3—813no—
147C2×D3—814no—
148C2×D3—811no—
149C2×D3—16212no—
150C2×D3—1624no—
151C3×C4—93no—
152C3×C4—91no—
153C3×C4—274no—
154Dic3—34no—
155Dic3—93no—
156Dic3—91no—
157C32—224no—
158C32—212no—
159C32—212no—
160C32—24no—
161C32—24no—
162C32(C3⋊D9)⋊C4112yescomplemented
163C32C4×C3⋊D911yescharacteristic, complemented
164C32#628914yes—
165C32#628911yescharacteristic
166C9—212no—
167C9#628913yescomplemented
168C2×C4—2431noSylow
169C2×C3—212no—
170C2×C3—24no—
171C2×C3D9×C3⋊D313yes—
172C2×C3D3×C3⋊D914yes—
173C2×C3C3⋊D3211yescharacteristic
174D3—816no—
175D3—818no—
176D3—812no—
177D3—16224no—
178D3—1628no—
179C22—2431no—
180C4—91no—
181C4—271no—
182C3—212no—
183C3—24no—
184C3#1061987013yescomplemented
185C3#1061987214yescomplemented
186C3#1062015011yescharacteristic
187C2—2432no—
188C2C3⋊D3×C3⋊D911yescharacteristic
subgroupG/H
center, hypercenterC2C3⋊D3×C3⋊D9
commutator, hypocenterC33×C9C2×C4
FrattiniC2×C3C3⋊D32
Fitting, cosocleC2×C33×C9C22
socleC2×C34C2×D3
prime radicalC2×C3⋊(C3⋊(C3⋊D9))C2
LCSG ▷ C33×C9
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3×C9×C3⋊Dic3C2semidirect
3. C32×C3⋊Dic9C2semidirect
8. C3⋊(C3⋊(C3⋊D9))C4semidirect
16. C9×C3⋊Dic3D3semidirect
17. C3×C3⋊Dic9D3semidirect
20. C33×C9C2×C4semidirect
42. C3×C3⋊Dic3D9semidirect
54. C3⋊Dic9C3⋊D3semidirect
60. C32×C9C4×D3semidirect
61. C32×C9C4×D3semidirect
101. C3⋊Dic3C3⋊D9semidirect
112. C33C4×D9semidirect
119. C3×C9#624semidirect
120. C3×C9C4×C3⋊D3semidirect
162. C32(C3⋊D9)⋊C4semidirect
163. C32C4×C3⋊D9semidirect
167. C9#6289semidirect
184. C3#10619870semidirect
185. C3#10619872semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊(C3⋊(C3⋊D9))2
C3×C9×C3⋊Dic32
C32×C3⋊Dic92
#106201503
#106198723
#106198703