Finite Group Databasebeta

← #14517032

Subgroups — #14517032

Order 1944.

312 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 58 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×#4176C211yesmaximal, characteristic
2C3⋊#66331C211yesmaximal, characteristic, complemented
3C3⋊#66324C211yesmaximal, characteristic, complemented
4#10619903—31nomaximal
5D3×C3⋊Dic9—31nomaximal
6#4176⋊C4—33nomaximal
7C2×C3×#731C2211yescharacteristic
8C3×#4176C412yescomplemented
9C2×C3×#272D311yescharacteristic
10C2×C3×D3×C9—31no—
11C3⋊(C3⋊Dic9)D311yescharacteristic, complemented
12C3⋊(3−1+2⋊C4)—61no—
13C3⋊((C3⋊Dic3)⋊C3)—31no—
14C3⋊((C3⋊Dic3)⋊C3)—31no—
15C3×C3⋊Dic9—31no—
16C2×#4176D313yes—
17#66331—33no—
18#66331—63no—
19#66324—33no—
20C3×#731C2×C411yescharacteristic, complemented, Sylow
21D3×C3⋊Dic3—91no—
22D3×C3⋊Dic3—91no—
23C2×C3⋊Dic9—91no—
24#6199—91no—
25D3×Dic9—93no—
26C2×C3×3−1+2—21no—
27C2×C3×H(3,𝔽3)C2×D311yescharacteristic
28C2×C32×C9C2×D311yescharacteristic
29C3×#272Dic312yes—
30C3×D3×C9—32no—
31C2×#731—23no—
32C2×#731C2×D313yes—
33#4176Dic316yescomplemented
34C2×C32×D3—31no—
35C2×C32×D3—91no—
36C3⋊(C3⋊Dic3)—31no—
37C3⋊(C3⋊Dic3)—31no—
38C3×C3⋊Dic3—91no—
39C3×C3⋊Dic3—91no—
40C22×C3×C9—91no—
41C2×#272C3⋊D311yescharacteristic
42C2×D3×C9—33no—
43C3⋊Dic9—31no—
44C3⋊Dic9—33no—
45C3⋊Dic9—61no—
46C3⋊Dic9—91no—
47C3⋊Dic9—181no—
483−1+2⋊C4—183no—
49(C3⋊Dic3)⋊C3—91no—
50(C3⋊Dic3)⋊C3—91no—
51(C3⋊Dic3)⋊C3—181no—
52(C3⋊Dic3)⋊C3—181no—
53C3×Dic9—93no—
54C3×3−1+2—21no—
55C3×H(3,𝔽3)C2×Dic311yescharacteristic
56C32×C9C4×D311yescharacteristic, complemented
57#731—23no—
58#731C2×Dic313yescomplemented
59C2×C3⋊Dic3—271no—
60D3×Dic3—271no—
61D3×Dic3—271no—
62D3×Dic3—273no—
63D3×Dic3—273no—
64C2×Dic9—273no—
65C2×C33—31no—
66C2×C33D3211yescharacteristic
67C32×D3—32no—
68C32×D3—92no—
69C2×3−1+2—23no—
70C2×3−1+2—121no—
71C2×H(3,𝔽3)—21no—
72C2×H(3,𝔽3)—61no—
73C2×H(3,𝔽3)C2×C3⋊D311yescharacteristic
74C2×C3×C9—31no—
75C2×C3×C9—61no—
76C2×C3×C9—61no—
77C2×C3×C9—92no—
78C2×C3×C9D3213yes—
79#272C3⋊Dic312yes—
80D3×C9—36no—
81C22×C32—91no—
82C2×C3×D3—33no—
83C2×C3×D3—31no—
84C2×C3×D3—91no—
85C2×C3×D3—93no—
86C3⋊Dic3—91no—
87C3⋊Dic3—91no—
88C3⋊Dic3—91no—
89C3⋊Dic3—91no—
90C3⋊Dic3—181no—
91C3⋊Dic3—181no—
92C3⋊Dic3—273no—
93C3⋊Dic3—273no—
94C3×Dic3—271no—
95C3×Dic3—273no—
96C3×Dic3—273no—
97C3×Dic3—271no—
98C22×C9—93no—
99Dic9—93no—
100Dic9—183no—
101Dic9—273no—
102C33—31no—
103C33D3×Dic311yescharacteristic
1043−1+2—23no—
1053−1+2—121no—
106H(3,𝔽3)—21no—
107H(3,𝔽3)—61no—
108H(3,𝔽3)C2×C3⋊Dic311yescharacteristic
109C3×C9—31no—
110C3×C9—61no—
111C3×C9—61no—
112C3×C9D3×Dic313yescomplemented
113C2×Dic3—811no—
114C2×Dic3—813no—
115C4×D3—811no—
116C4×D3—811no—
117C2×C32—21no—
118C2×C32—33no—
119C2×C32—31no—
120C2×C32—61no—
121C2×C32—92no—
122C2×C32—93no—
123C2×C32((C3⋊D3)⋊C3)⋊C211yescharacteristic
124C2×C32D3×C3⋊D311yescharacteristic
125C3×D3—36no—
126C3×D3—32no—
127C3×D3—92no—
128C3×D3—96no—
129C2×C9—33no—
130C2×C9—63no—
131C2×C9—96no—
132C22×C3—93no—
133C22×C3—91no—
134C2×D3—31no—
135C2×D3—91no—
136C3×C4—811no—
137C3×C4—811no—
138Dic3—273no—
139Dic3—273no—
140Dic3—271no—
141Dic3—271no—
142Dic3—811no—
143Dic3—811no—
144Dic3—1621no—
145Dic3—1621no—
146C32—21no—
147C32—33no—
148C32—31no—
149C32—61no—
150C32—93no—
151C32((C3⋊D3)⋊C3)⋊C411yescharacteristic
152C32D3×C3⋊Dic311yescharacteristic
153C9—33no—
154C9—63no—
155C2×C4—2431noSylow
156C2×C3—31no—
157C2×C3—61no—
158C2×C3—96no—
159C2×C3—92no—
160C2×C3—91no—
161C2×C3—181no—
162C2×C3#4176⋊C213yes—
163C2×C3((C3⋊D3)⋊C3)⋊D311yescharacteristic
164D3—32no—
165D3—92no—
166C22—91no—
167C4—811no—
168C4—811no—
169C3—31no—
170C3—61no—
171C3—91no—
172C3—181no—
173C3#4176⋊C413yescomplemented
174C3((C3⋊D3)⋊C3)⋊Dic311yescharacteristic
175C2—92no—
176C2#1175773811yescharacteristic
subgroupG/H
center, hypercenterC2#11757738
commutator, hypocenterC3×#731C2×C4
FrattiniC2×C32D3×C3⋊D3
Fitting, cosocleC2×C3×#731C22
socleC2×C32((C3⋊D3)⋊C3)⋊C2
prime radicalC2×C3×#272D3
LCSG ▷ C3×#731
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3⋊#66331C2semidirect
3. C3⋊#66324C2semidirect
8. C3×#4176C4semidirect
11. C3⋊(C3⋊Dic9)D3semidirect
20. C3×#731C2×C4semidirect
33. #4176Dic3semidirect
56. C32×C9C4×D3semidirect
58. #731C2×Dic3semidirect
112. C3×C9D3×Dic3semidirect
173. C3#4176⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#41762
C3⋊#663312
C3⋊#663242
#106199033
D3×C3⋊Dic93
#4176⋊C43