Finite Group Databasebeta

← #14517037

Subgroups — #14517037

Order 1944.

320 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 50 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⋊#4177C211yesmaximal, characteristic
2C3⋊#66331C211yesmaximal, characteristic, complemented
3C3×#66323C211yesmaximal, characteristic, complemented
4#10619901—31nomaximal
5#10619872—31nomaximal
6#4177⋊C4—33nomaximal
7C2×C3×#731C2211yescharacteristic
8C3⋊#4177C412yescomplemented
9C2×C3⋊(C3⋊D9)D311yescharacteristic
10C2×C3⋊((C3⋊D3)⋊C3)—31no—
11C3⋊(3−1+2⋊C4)—61no—
12C3×#1084D311yescharacteristic
13C3⋊((C3⋊Dic3)⋊C3)—31no—
14C3×C3⋊Dic9—31no—
15C3×C9×Dic3—31no—
16C2×#4177—33no—
17#66331—33no—
18#66331—63no—
19#66323D313yescomplemented
20C3×#731C2×C411yescharacteristic, complemented, Sylow
21#6289—91no—
22Dic3×C3⋊D3—91no—
23C4×C3⋊D9—91no—
24((C3⋊D3)⋊C3)⋊C4—91no—
25(C3⋊D9)⋊C4—93no—
26C2×C3×3−1+2—21no—
27C2×C3×H(3,𝔽3)C2×D311yescharacteristic
28C2×C32×C9C2×D311yescharacteristic
29C3⋊(C3⋊D9)Dic312yescomplemented
30C3⋊((C3⋊D3)⋊C3)—32no—
31C2×#731—23no—
32C2×#731C2×D313yes—
33#4177—36no—
34C2×C3⋊(C3⋊D3)—31no—
35C2×C3×C3⋊D3—91no—
36C3⋊(C3⋊Dic3)—31no—
37C3×C3⋊Dic3—91no—
38C32×Dic3—31no—
39C32×Dic3—91no—
40C2×C3⋊D9—33no—
41C2×C3⋊D9—91no—
42C2×C3⋊D9—181no—
43C2×(C3⋊D3)⋊C3—91no—
44C2×(C3⋊D3)⋊C3—181no—
45C3×C4×C9—91no—
46#1084C3⋊D311yescharacteristic
47C3⋊Dic9—31no—
48C3⋊Dic9—61no—
493−1+2⋊C4—183no—
50(C3⋊Dic3)⋊C3—91no—
51(C3⋊Dic3)⋊C3—181no—
52C9×Dic3—33no—
53C3×Dic9—93no—
54C3×3−1+2—21no—
55C3×H(3,𝔽3)C4×D311yescharacteristic
56C32×C9C2×Dic311yescharacteristic, complemented
57#731—23no—
58#731C4×D313yescomplemented
59C4×C3⋊D3—271no—
60#624—271no—
61#624—273no—
62D3×Dic3—271no—
63D3×Dic3—273no—
64C4×D9—273no—
65C2×C33—31no—
66C2×C33D3211yescharacteristic
67C3⋊(C3⋊D3)—32no—
68C3×C3⋊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×C9D3213yes—
78C3⋊D9—36no—
79C3⋊D9—92no—
80C3⋊D9—182no—
81(C3⋊D3)⋊C3—92no—
82(C3⋊D3)⋊C3—182no—
83C2×C3⋊D3—91no—
84C2×C3⋊D3—91no—
85C2×C3⋊D3—181no—
86C2×C3⋊D3—273no—
87C2×C3×D3—271no—
88C2×C3×D3—273no—
89C32×C4—91no—
90C3⋊Dic3—91no—
91C3⋊Dic3—91no—
92C3⋊Dic3—181no—
93C3⋊Dic3—273no—
94C3×Dic3—33no—
95C3×Dic3—31no—
96C3×Dic3—91no—
97C3×Dic3—93no—
98C3×Dic3—273no—
99C3×Dic3—271no—
100C2×D9—273no—
101C4×C9—93no—
102Dic9—93no—
103Dic9—183no—
104C33—31no—
105C33D3×Dic311yescharacteristic
1063−1+2—23no—
1073−1+2—121no—
108H(3,𝔽3)—21no—
109H(3,𝔽3)—61no—
110H(3,𝔽3)C4×C3⋊D311yescharacteristic
111C3×C9—31no—
112C3×C9—61no—
113C3×C9—61no—
114C3×C9D3×Dic313yescomplemented
115C2×Dic3—811no—
116C4×D3—811no—
117C4×D3—811no—
118C4×D3—813no—
119C2×C32—21no—
120C2×C32—33no—
121C2×C32—31no—
122C2×C32—61no—
123C2×C32—93no—
124C2×C32((C3⋊D3)⋊C3)⋊C211yescharacteristic
125C2×C32D3×C3⋊D311yescharacteristic
126C3⋊D3—92no—
127C3⋊D3—92no—
128C3⋊D3—182no—
129C3⋊D3—276no—
130C3×D3—272no—
131C3×D3—276no—
132C2×C9—33no—
133C2×C9—63no—
134D9—276no—
135C22×C3—811no—
136C2×D3—273no—
137C2×D3—271no—
138C2×D3—811no—
139C2×D3—1621no—
140C3×C4—93no—
141C3×C4—91no—
142C3×C4—811no—
143Dic3—31no—
144Dic3—91no—
145Dic3—273no—
146Dic3—271no—
147Dic3—811no—
148Dic3—1621no—
149C32—21no—
150C32—33no—
151C32—31no—
152C32—61no—
153C32—93no—
154C32((C3⋊D3)⋊C3)⋊C411yescharacteristic
155C32Dic3×C3⋊D311yescharacteristic
156C9—33no—
157C9—63no—
158C2×C4—2431noSylow
159C2×C3—31no—
160C2×C3—61no—
161C2×C3—91no—
162C2×C3—181no—
163C2×C3—812no—
164C2×C3#4176⋊C213yes—
165C2×C3((C3⋊D3)⋊C3)⋊D311yescharacteristic
166D3—276no—
167D3—272no—
168D3—812no—
169D3—1622no—
170C22—811no—
171C4—91no—
172C4—811no—
173C3—31no—
174C3—61no—
175C3—91no—
176C3—181no—
177C3#4177⋊C413yescomplemented
178C3#1061988311yescharacteristic
179C2—812no—
180C2#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⋊#4177C2
LCSG ▷ C3×#731
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3⋊#66331C2semidirect
3. C3×#66323C2semidirect
8. C3⋊#4177C4semidirect
19. #66323D3semidirect
20. C3×#731C2×C4semidirect
29. C3⋊(C3⋊D9)Dic3semidirect
56. C32×C9C2×Dic3semidirect
58. #731C4×D3semidirect
114. C3×C9D3×Dic3semidirect
177. C3#4177⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊#41772
C3⋊#663312
C3×#663232
#106199013
#106198723
#4177⋊C43