Finite Group Databasebeta

← C2×#66331⋊C3 #14517713

Subgroups — C2×#66331⋊C3 #14517713

Order 1944.

390 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C22×#6910C211yesmaximal, characteristic
2#66331⋊C3C212yesmaximal, direct product factor
3C2×C3×3−1+2⋊C4—32nomaximal
4C2×C3×3−1+2⋊C4—31nomaximal
5C2×C3×(C3⋊Dic3)⋊C3—31nomaximal
6C2×#66331C311yesmaximal, characteristic, complemented
7C2×#6910C412yescomplemented
8C2×#6910C2211yescharacteristic
9C22×C3×3−1+2D311yescharacteristic
10C22×C3×3−1+2D312yes—
11C22×C3×H(3,𝔽3)D311yescharacteristic
12C3×3−1+2⋊C4—34no—
13C3×3−1+2⋊C4—32no—
14C3×(C3⋊Dic3)⋊C3—32no—
15C22×#731—22no—
16C22×#731—21no—
17C22×#731—21no—
18C22×#731C2×C311yescharacteristic
19#66331C2×C312yescomplemented
20#6910C2×C411yescharacteristic, complemented, Sylow
21C2×C3×C3⋊Dic3—31no—
22C2×C32×Dic3—91no—
23C2×3−1+2⋊C4—32no—
24C2×3−1+2⋊C4—32no—
25C2×3−1+2⋊C4—32no—
26C2×3−1+2⋊C4—31no—
27C2×3−1+2⋊C4—32no—
28C2×(C3⋊Dic3)⋊C3—32no—
29C2×(C3⋊Dic3)⋊C3—31no—
30C2×C3×Dic9—32no—
31C2×C3×Dic9—31no—
32C2×C3×3−1+2Dic312yescomplemented
33C2×C3×3−1+2Dic314yescomplemented
34C2×C3×3−1+2C2×D311yescharacteristic
35C2×C3×3−1+2C2×D312yes—
36C2×C3×H(3,𝔽3)Dic312yes—
37C2×C3×H(3,𝔽3)C2×D311yescharacteristic
38C2×#731—24no—
39C2×#731—22no—
40C2×#731—22no—
41C2×#731—21no—
42C2×#731—22no—
43C2×#731—21no—
44C2×#731C3×C412yescomplemented
45C2×#731C22×C311yescharacteristic
46C22×C33—31no—
47C22×C33C3⋊D311yescharacteristic
48C3×C3⋊Dic3—32no—
49C32×Dic3—92no—
50C22×3−1+2—22no—
51C22×3−1+2—32no—
52C22×3−1+2—32no—
53C22×3−1+2—32no—
54C22×3−1+2—31no—
55C22×3−1+2C3×D312yes—
56C22×H(3,𝔽3)—21no—
57C22×H(3,𝔽3)—32no—
58C22×H(3,𝔽3)C3×D311yescharacteristic
59C22×C3×C9—21no—
60C22×C3×C9—32no—
61C22×C3×C9C3×D311yescharacteristic
623−1+2⋊C4—34no—
633−1+2⋊C4—34no—
643−1+2⋊C4—34no—
653−1+2⋊C4—32no—
663−1+2⋊C4—34no—
67(C3⋊Dic3)⋊C3—34no—
68(C3⋊Dic3)⋊C3—32no—
69C3×Dic9—34no—
70C3×Dic9—32no—
71C3×3−1+2C2×Dic311yescharacteristic, complemented
72C3×3−1+2C2×Dic312yescomplemented
73C3×H(3,𝔽3)C2×Dic311yescharacteristic
74#731—22no—
75#731—21no—
76#731—21no—
77#731C2×C3×C411yescharacteristic, complemented
78C2×C32×C4—271no—
79C2×C3⋊Dic3—31no—
80C2×C3×Dic3—92no—
81C2×C3×Dic3—91no—
82C2×C3×Dic3—91no—
83C2×C3×Dic3—271no—
84C2×Dic9—32no—
85C2×Dic9—31no—
86C2×C33—32no—
87C2×C33—31no—
88C2×C33C3⋊Dic312yes—
89C2×C33C2×C3⋊D311yescharacteristic
90C2×3−1+2—24no—
91C2×3−1+2—22no—
92C2×3−1+2—34no—
93C2×3−1+2—34no—
94C2×3−1+2—34no—
95C2×3−1+2—32no—
96C2×3−1+2—32no—
97C2×3−1+2—32no—
98C2×3−1+2—32no—
99C2×3−1+2—31no—
100C2×3−1+2C3×Dic314yescomplemented
101C2×3−1+2C2×C3×D312yes—
102C2×H(3,𝔽3)—22no—
103C2×H(3,𝔽3)—21no—
104C2×H(3,𝔽3)—34no—
105C2×H(3,𝔽3)—32no—
106C2×H(3,𝔽3)C3×Dic312yes—
107C2×H(3,𝔽3)C2×C3×D311yescharacteristic
108C2×C3×C9—22no—
109C2×C3×C9—21no—
110C2×C3×C9—34no—
111C2×C3×C9—32no—
112C2×C3×C9C3×Dic312yescomplemented
113C2×C3×C9C2×C3×D311yescharacteristic
114C22×C32—31no—
115C22×C32—61no—
116C22×C32—91no—
117C22×C32—91no—
118C22×C32—181no—
119C22×C32#27212yes—
120C22×C32#27211yescharacteristic
121C22×C32C3×C3⋊D311yescharacteristic
122C32×C4—272no—
123C3⋊Dic3—32no—
124C3×Dic3—94no—
125C3×Dic3—92no—
126C3×Dic3—92no—
127C3×Dic3—272no—
128C22×C9—32no—
129C22×C9—31no—
130C22×C9—61no—
131C22×C9—62no—
132Dic9—34no—
133Dic9—32no—
134C33—31no—
135C33C2×C3⋊Dic311yescharacteristic
1363−1+2—22no—
1373−1+2—32no—
1383−1+2—32no—
1393−1+2—32no—
1403−1+2—31no—
1413−1+2C2×C3×Dic312yescomplemented
142H(3,𝔽3)—21no—
143H(3,𝔽3)—32no—
144H(3,𝔽3)C2×C3×Dic311yescharacteristic
145C3×C9—21no—
146C3×C9—32no—
147C3×C9C2×C3×Dic311yescharacteristic, complemented
148C2×C3×C4—271no—
149C2×C3×C4—272no—
150C2×C3×C4—271no—
151C2×Dic3—91no—
152C2×Dic3—271no—
153C2×C32—32no—
154C2×C32—31no—
155C2×C32—62no—
156C2×C32—61no—
157C2×C32—92no—
158C2×C32—91no—
159C2×C32—91no—
160C2×C32—92no—
161C2×C32—182no—
162C2×C32—181no—
163C2×C32#108414yes—
164C2×C32#108412yes—
165C2×C32C2×#27212yes—
166C2×C32C2×#27211yescharacteristic
167C2×C32C3×C3⋊Dic312yes—
168C2×C32C2×C3×C3⋊D311yescharacteristic
169C2×C9—34no—
170C2×C9—32no—
171C2×C9—32no—
172C2×C9—31no—
173C2×C9—62no—
174C2×C9—64no—
175C2×C9—61no—
176C2×C9—62no—
177C22×C3—31no—
178C22×C3—32no—
179C22×C3—31no—
180C22×C3—91no—
181C22×C3—181no—
182C22×C3C3×#27211yescharacteristic
183C3×C4—272no—
184C3×C4—274no—
185C3×C4—272no—
186Dic3—92no—
187Dic3—272no—
188C32—31no—
189C32—61no—
190C32—91no—
191C32—91no—
192C32—181no—
193C32C2×#108412yes—
194C32C2×#108411yescharacteristic
195C32C2×C3×C3⋊Dic311yescharacteristic
196C9—32no—
197C9—31no—
198C9—61no—
199C9—62no—
200C2×C4—271noSylow
201C2×C3—32no—
202C2×C3—34no—
203C2×C3—32no—
204C2×C3—31no—
205C2×C3—32no—
206C2×C3—31no—
207C2×C3—92no—
208C2×C3—91no—
209C2×C3—182no—
210C2×C3—181no—
211C2×C3C3×#108412yes—
212C2×C3C2×C3×#27211yescharacteristic
213C22#4184⋊C311yescharacteristic
214C4—272no—
215C3—31no—
216C3—32no—
217C3—31no—
218C3—91no—
219C3—181no—
220C3C2×C3×#108411yescharacteristic
221C2#66331⋊C312yesdirect product factor
222C2C2×#4184⋊C311yescharacteristic
subgroupG/H
center, hypercenterC22#4184⋊C3
commutator, hypocenter#731C2×C3×C4
FrattiniC2×C32C2×C3×C3⋊D3
FittingC22×#6910C2
socleC22×C3C3×#272
prime radicalC22×C3×H(3,𝔽3)D3
cosocleC2×#731C22×C3
LCSG ▷ #731
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. #66331⋊C3C2direct (N × H)
6. C2×#66331C3semidirect
7. C2×#6910C4semidirect
19. #66331C2×C3semidirect
20. #6910C2×C4semidirect
32. C2×C3×3−1+2Dic3semidirect
33. C2×C3×3−1+2Dic3semidirect
44. C2×#731C3×C4semidirect
71. C3×3−1+2C2×Dic3semidirect
72. C3×3−1+2C2×Dic3semidirect
77. #731C2×C3×C4semidirect
100. C2×3−1+2C3×Dic3semidirect
112. C2×C3×C9C3×Dic3semidirect
141. 3−1+2C2×C3×Dic3semidirect
147. C3×C9C2×C3×Dic3semidirect
221. C2#66331⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#69102
#66331⋊C32
C2×C3×3−1+2⋊C43
C2×C3×(C3⋊Dic3)⋊C33
C2×#663313