Finite Group Databasebeta

← #14517034

Subgroups — #14517034

Order 1944.

318 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 44 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⋊#4184C211yesmaximal, characteristic
2C3⋊#66323C211yesmaximal, characteristic, complemented
3C3×#66324C211yesmaximal, characteristic, complemented
4#10619896—31nomaximal
5#10619883—31nomaximal
6#4184⋊C4—33nomaximal
7C2×C3×#731C2211yescharacteristic
8C3⋊#4184C412yescomplemented
9C2×C3⋊AGL(1,ℤ/9)—61no—
10C2×C3⋊((C3⋊D3)⋊C3)—31no—
11C2×C3×C3⋊D9—31no—
12C3⋊#1084D311yescharacteristic
13C9×C3⋊Dic3—31no—
14C3×C3⋊Dic9D311yescharacteristic, complemented
15C3×(C3⋊Dic3)⋊C3—31no—
16C2×#4184—33no—
17C2×#4184—63no—
18#66324D313yescomplemented
19#66323—33no—
20C3×#731C2×C411yescharacteristic, complemented, Sylow
21#6294—91no—
22#6289—91no—
23((C3⋊D3)⋊C3)⋊C4—93no—
24(C3⋊D9)⋊C4—91no—
25Dic3×D9—91no—
26C2×C3×3−1+2—21no—
27C2×C3×H(3,𝔽3)C2×D311yescharacteristic
28C2×C32×C9C2×D311yescharacteristic
29C3⋊AGL(1,ℤ/9)—62no—
30C3⋊((C3⋊D3)⋊C3)—32no—
31C3×C3⋊D9—32no—
32C2×#731—23no—
33C2×#731C2×D313yes—
34#4184—36no—
35#4184—66no—
36C2×C3⋊(C3⋊D3)—31no—
37C2×C3×C3⋊D3—91no—
38C3×C3⋊Dic3—31no—
39C3×C3⋊Dic3—31no—
40C3×C3⋊Dic3—91no—
41C32×Dic3—91no—
42C2×C3⋊D9—31no—
43C2×C3⋊D9—61no—
44C2×AGL(1,ℤ/9)—183no—
45C2×(C3⋊D3)⋊C3—93no—
46C2×C3×D9—91no—
47C2×C3×D9—181no—
48#1084—33no—
49#1084—181no—
50C3⋊Dic9C3⋊D311yescharacteristic, complemented
51(C3⋊Dic3)⋊C3—33no—
52C9×Dic3—91no—
53C9×Dic3—91no—
54C9×Dic3—181no—
55C3×Dic9—91no—
56C3×3−1+2—21no—
57C3×H(3,𝔽3)C4×D311yescharacteristic
58C32×C9C4×D311yescharacteristic, complemented
59#731—23no—
60#731C4×D313yescomplemented
61C4×C3⋊D3—271no—
62#624—271no—
63#624—273no—
64D3×Dic3—271no—
65D3×Dic3—271no—
66C4×D9—271no—
67C2×C33—31no—
68C2×C33D3211yescharacteristic
69C3⋊(C3⋊D3)—32no—
70C3×C3⋊D3—92no—
71C2×3−1+2—23no—
72C2×3−1+2—121no—
73C2×H(3,𝔽3)—61no—
74C2×H(3,𝔽3)D3213yes—
75C2×C3×C9—21no—
76C2×C3×C9—31no—
77C2×C3×C9—61no—
78C2×C3×C9—61no—
79C2×C3×C9C2×C3⋊D311yescharacteristic
80C3⋊D9—32no—
81C3⋊D9—62no—
82AGL(1,ℤ/9)—186no—
83(C3⋊D3)⋊C3—96no—
84C3×D9—92no—
85C3×D9—182no—
86C2×C3⋊D3—91no—
87C2×C3⋊D3—93no—
88C2×C3⋊D3—271no—
89C2×C3⋊D3—541no—
90C2×C3×D3—271no—
91C2×C3×D3—271no—
92C2×C3×D3—541no—
93C32×C4—271no—
94C3⋊Dic3—31no—
95C3⋊Dic3—31no—
96C3⋊Dic3—91no—
97C3×Dic3—93no—
98C3×Dic3—91no—
99C3×Dic3—91no—
100C3×Dic3—91no—
101C3×Dic3—181no—
102C3×Dic3—273no—
103C3×Dic3—271no—
104C2×D9—91no—
105C2×D9—181no—
106C2×D9—183no—
107C4×C9—271no—
108Dic9—91no—
109C33—31no—
110C33#62411yescharacteristic
1113−1+2—23no—
1123−1+2—121no—
113H(3,𝔽3)—61no—
114H(3,𝔽3)#62413yes—
115C3×C9—21no—
116C3×C9—31no—
117C3×C9—61no—
118C3×C9—61no—
119C3×C9C4×C3⋊D311yescharacteristic, complemented
120C2×Dic3—811no—
121C4×D3—811no—
122C4×D3—811no—
123C4×D3—813no—
124C2×C32—21no—
125C2×C32—31no—
126C2×C32—33no—
127C2×C32—61no—
128C2×C32—91no—
129C2×C32—181no—
130C2×C32((C3⋊D3)⋊C3)⋊C211yescharacteristic
131C2×C32D3×C3⋊D311yescharacteristic
132C3⋊D3—92no—
133C3⋊D3—96no—
134C3⋊D3—272no—
135C3⋊D3—542no—
136C3×D3—272no—
137C3×D3—272no—
138C3×D3—542no—
139C2×C9—31no—
140C2×C9—61no—
141C2×C9—63no—
142D9—92no—
143D9—182no—
144D9—186no—
145C22×C3—811no—
146C2×D3—271no—
147C2×D3—271no—
148C2×D3—541no—
149C2×D3—813no—
150C3×C4—273no—
151C3×C4—271no—
152C3×C4—271no—
153Dic3—91no—
154Dic3—91no—
155Dic3—91no—
156Dic3—181no—
157Dic3—271no—
158Dic3—273no—
159C32—21no—
160C32—31no—
161C32—33no—
162C32—61no—
163C32—91no—
164C32—181no—
165C32#619911yescharacteristic
166C32#628911yescharacteristic
167C9—31no—
168C9—61no—
169C9—63no—
170C2×C4—2431noSylow
171C2×C3—21no—
172C2×C3—31no—
173C2×C3—61no—
174C2×C3—93no—
175C2×C3—812no—
176C2×C3#4176⋊C211yescharacteristic
177C2×C3((C3⋊D3)⋊C3)⋊D311yescharacteristic
178D3—272no—
179D3—272no—
180D3—542no—
181D3—816no—
182C22—811no—
183C4—271no—
184C4—271no—
185C3—21no—
186C3—31no—
187C3—61no—
188C3—93no—
189C3#4184⋊C411yescharacteristic, complemented
190C3#1061988511yescharacteristic
191C2—812no—
192C2#4177⋊D311yescharacteristic
subgroupG/H
center, hypercenterC2#4177⋊D3
commutator, hypocenterC3×#731C2×C4
FrattiniC2×C32D3×C3⋊D3
Fitting, cosocleC2×C3×#731C22
socleC2×C32((C3⋊D3)⋊C3)⋊C2
prime radicalC2×C3⋊#4184C2
LCSG ▷ C3×#731
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3⋊#66323C2semidirect
3. C3×#66324C2semidirect
8. C3⋊#4184C4semidirect
14. C3×C3⋊Dic9D3semidirect
18. #66324D3semidirect
20. C3×#731C2×C4semidirect
50. C3⋊Dic9C3⋊D3semidirect
58. C32×C9C4×D3semidirect
60. #731C4×D3semidirect
119. C3×C9C4×C3⋊D3semidirect
189. C3#4184⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊#41842
C3⋊#663232
C3×#663242
#106198963
#106198833
#4184⋊C43