Finite Group Databasebeta

← #14517033

Subgroups — #14517033

Order 1944.

294 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 46 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#10619898—31nomaximal
5#10619885—31nomaximal
6#4176⋊C4—33nomaximal
7C2×C3×#731C2211yescharacteristic
8C3⋊#4176C412yescomplemented
9C2×C3⋊#272D311yescharacteristic
10C2×C9×C3⋊D3—31no—
11C3⋊(3−1+2⋊C4)—61no—
12C3⋊((C3⋊Dic3)⋊C3)—31no—
13C3×C3⋊Dic9—31no—
14C3×C3⋊Dic9D311yescharacteristic, complemented
15C3×(C3⋊Dic3)⋊C3—31no—
16C2×#4176—33no—
17#66331—33no—
18#66331—63no—
19#66324D313yescomplemented
20C3×#731C2×C411yescharacteristic, complemented, Sylow
21#6294—91no—
22Dic3×C3⋊D3—91no—
23#6199—93no—
24D3×Dic9—91no—
25D3×Dic9—91no—
26C2×C3×3−1+2—21no—
27C2×C3×H(3,𝔽3)C2×D311yescharacteristic
28C2×C32×C9C2×D311yescharacteristic
29C3⋊#272Dic312yes—
30C9×C3⋊D3—32no—
31C2×#731—23no—
32C2×#731C2×D313yes—
33#4176—36no—
34C2×C3×C3⋊D3—31no—
35C2×C3×C3⋊D3—91no—
36C3⋊(C3⋊Dic3)—31no—
37C3×C3⋊Dic3—31no—
38C3×C3⋊Dic3—91no—
39C32×Dic3—91no—
40C2×#272—33no—
41C2×#272—181no—
42C2×D3×C9—91no—
43C2×D3×C9—91no—
44C2×D3×C9—181no—
45C3⋊Dic9—31no—
46C3⋊Dic9—61no—
47C3⋊Dic9C3⋊D311yescharacteristic, complemented
483−1+2⋊C4—183no—
49(C3⋊Dic3)⋊C3—33no—
50(C3⋊Dic3)⋊C3—93no—
51C3×Dic9—91no—
52C3×Dic9—91no—
53C3×Dic9—181no—
54C3×3−1+2—21no—
55C3×H(3,𝔽3)C2×Dic311yescharacteristic
56C32×C9C4×D311yescharacteristic, complemented
57#731—23no—
58#731C4×D313yescomplemented
59C4×C3⋊D3—271no—
60#624—271no—
61D3×Dic3—271no—
62D3×Dic3—273no—
63D3×Dic3—271no—
64C2×Dic9—271no—
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)—61no—
72C2×H(3,𝔽3)D3213yes—
73C2×C3×C9—21no—
74C2×C3×C9—31no—
75C2×C3×C9—61no—
76C2×C3×C9—61no—
77C2×C3×C9C2×C3⋊D311yescharacteristic
78#272—36no—
79#272—182no—
80D3×C9—92no—
81D3×C9—92no—
82D3×C9—182no—
83C2×C3⋊D3—31no—
84C2×C3⋊D3—91no—
85C2×C3×D3—91no—
86C2×C3×D3—91no—
87C2×C3×D3—181no—
88C2×C3×D3—273no—
89C32×C4—271no—
90C3⋊Dic3—31no—
91C3⋊Dic3—91no—
92C3⋊Dic3—93no—
93C3⋊Dic3—271no—
94C3⋊Dic3—541no—
95C3×Dic3—93no—
96C3×Dic3—91no—
97C3×Dic3—271no—
98C3×Dic3—271no—
99C3×Dic3—271no—
100C3×Dic3—541no—
101C22×C9—271no—
102Dic9—91no—
103Dic9—91no—
104Dic9—181no—
105Dic9—183no—
106C33—31no—
107C33D3×Dic311yescharacteristic
1083−1+2—23no—
1093−1+2—121no—
110H(3,𝔽3)—61no—
111H(3,𝔽3)D3×Dic313yes—
112C3×C9—21no—
113C3×C9—31no—
114C3×C9—61no—
115C3×C9—61no—
116C3×C9C4×C3⋊D311yescharacteristic, complemented
117C2×Dic3—811no—
118C4×D3—811no—
119C4×D3—811no—
120C4×D3—813no—
121C2×C32—21no—
122C2×C32—31no—
123C2×C32—33no—
124C2×C32—61no—
125C2×C32—91no—
126C2×C32—181no—
127C2×C32((C3⋊D3)⋊C3)⋊C211yescharacteristic
128C2×C32D3×C3⋊D311yescharacteristic
129C3⋊D3—32no—
130C3⋊D3—92no—
131C3×D3—92no—
132C3×D3—92no—
133C3×D3—182no—
134C3×D3—276no—
135C2×C9—31no—
136C2×C9—61no—
137C2×C9—63no—
138C2×C9—272no—
139C22×C3—271no—
140C2×D3—91no—
141C2×D3—91no—
142C2×D3—181no—
143C2×D3—273no—
144C3×C4—273no—
145C3×C4—271no—
146C3×C4—811no—
147Dic3—91no—
148Dic3—271no—
149Dic3—271no—
150Dic3—271no—
151Dic3—541no—
152Dic3—813no—
153C32—21no—
154C32—31no—
155C32—33no—
156C32—61no—
157C32—91no—
158C32—181no—
159C32((C3⋊D3)⋊C3)⋊C411yescharacteristic
160C32Dic3×C3⋊D311yescharacteristic
161C9—31no—
162C9—61no—
163C9—63no—
164C2×C4—2431noSylow
165C2×C3—21no—
166C2×C3—31no—
167C2×C3—61no—
168C2×C3—93no—
169C2×C3—272no—
170C2×C3#4176⋊C211yescharacteristic
171C2×C3((C3⋊D3)⋊C3)⋊D311yescharacteristic
172D3—92no—
173D3—92no—
174D3—182no—
175D3—276no—
176C22—271no—
177C4—271no—
178C4—811no—
179C3—21no—
180C3—31no—
181C3—61no—
182C3—93no—
183C3#4176⋊C411yescharacteristic, complemented
184C3#1061988311yescharacteristic
185C2—272no—
186C2#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⋊#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
14. C3×C3⋊Dic9D3semidirect
19. #66324D3semidirect
20. C3×#731C2×C4semidirect
47. C3⋊Dic9C3⋊D3semidirect
56. C32×C9C4×D3semidirect
58. #731C4×D3semidirect
116. C3×C9C4×C3⋊D3semidirect
183. 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
#106198983
#106198853
#4176⋊C43