Finite Group Databasebeta

← #10619650⋊C3 #14517481

Subgroups — #10619650⋊C3 #14517481

Order 1944.

354 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 63 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×#6911C211yesmaximal, characteristic, complemented
2C2×#4179⋊C3C211yesmaximal, characteristic, complemented
3#66326⋊C3C211yesmaximal, characteristic, complemented
4#10619980C311yesmaximal, characteristic, complemented
5C3×#638⋊C3—31nomaximal
6#10619650C313yesmaximal, complemented
7C2×#6911—21no—
8C2×#6911C2211yescharacteristic
9#4179⋊C3—21no—
10C22×C3×3−1+2C2×C311yescharacteristic, complemented
11C22×C3×H(3,𝔽3)—21no—
12C22×C3×H(3,𝔽3)D311yescharacteristic
13C2×C3⋊AGL(1,ℤ/9)C2×C311yescharacteristic, complemented
14C2×C3×(C3⋊D3)⋊C3—31no—
15C3⋊(3−1+2⋊C4)C2×C311yescharacteristic, complemented
16C3×(C3⋊Dic3)⋊C3—31no—
17C22×#732—23no—
18C22×#732C2×C313yescomplemented
19C2×#4179C2×C313yescomplemented
20#66326C2×C313yescomplemented
21#6911D411yescharacteristic, complemented, Sylow
22C3×#638—31no—
23C32×#67—91no—
24#6233C3211yescharacteristic, complemented
25#611⋊C3—91no—
26#638⋊C3—33no—
27C2×C3×3−1+2—21no—
28C2×C3×3−1+2C22×C311yescharacteristic
29C2×C3×H(3,𝔽3)—22no—
30C2×C3×H(3,𝔽3)—21no—
31C2×C3×H(3,𝔽3)—21no—
32C2×C3×H(3,𝔽3)C2×D311yescharacteristic
33C3⋊AGL(1,ℤ/9)—21no—
34C3×(C3⋊D3)⋊C3—61no—
35C2×#732—26no—
36C2×#732—23no—
37C2×#732—23no—
38C2×#732C22×C313yes—
39#4179—23no—
40C22×C33—31no—
41C22×C33—61no—
42C22×C33C3×D311yescharacteristic
43C2×C3×C3⋊D3—31no—
44C2×C32×D3—91no—
45C3×C3⋊Dic3—31no—
46C32×Dic3—91no—
47C22×3−1+2—31no—
48C22×3−1+2—61no—
49C22×H(3,𝔽3)—23no—
50C22×H(3,𝔽3)—61no—
51C22×H(3,𝔽3)—61no—
52C22×H(3,𝔽3)—61no—
53C22×H(3,𝔽3)C3×D313yes—
54C22×C3×C9—21no—
55C22×C3×C9C2×C3211yescharacteristic, complemented
56C2×C3⋊D9C2×C3211yescharacteristic, complemented
57C2×AGL(1,ℤ/9)—91no—
58C2×(C3⋊D3)⋊C3—33no—
59C3⋊Dic9C2×C3211yescharacteristic, complemented
603−1+2⋊C4—91no—
61(C3⋊Dic3)⋊C3—33no—
62C3×3−1+2C3×D411yescharacteristic, complemented
63C3×H(3,𝔽3)—21no—
64C3×H(3,𝔽3)#6711yescharacteristic
65#732—23no—
66#732C3×D413yescomplemented
67C32×D4—271no—
68#638—31no—
69C3×#67—93no—
70C3×#67—91no—
71C3×#67—271no—
72#611—91no—
73C2×C33—21no—
74C2×C33—31no—
75C2×C33—61no—
76C2×C33—62no—
77C2×C33—61no—
78C2×C33C2×C3×D311yescharacteristic
79C3×C3⋊D3—61no—
80C32×D3—181no—
81C2×3−1+2—31no—
82C2×3−1+2—61no—
83C2×3−1+2—61no—
84C2×3−1+2—62no—
85C2×H(3,𝔽3)—26no—
86C2×H(3,𝔽3)—23no—
87C2×H(3,𝔽3)—23no—
88C2×H(3,𝔽3)—61no—
89C2×H(3,𝔽3)—62no—
90C2×H(3,𝔽3)—62no—
91C2×H(3,𝔽3)—62no—
92C2×H(3,𝔽3)—61no—
93C2×H(3,𝔽3)—61no—
94C2×H(3,𝔽3)C2×C3×D313yes—
95C2×C3×C9—22no—
96C2×C3×C9—21no—
97C2×C3×C9—21no—
98C2×C3×C9C22×C3211yescharacteristic
99C3⋊D9—21no—
100AGL(1,ℤ/9)—181no—
101(C3⋊D3)⋊C3—63no—
102C22×C32—21no—
103C22×C32—33no—
104C22×C32—63no—
105C22×C32—91no—
106C22×C32—91no—
107C22×C32—181no—
108C22×C32—183no—
109C22×C32—271no—
110C22×C32(C3⋊D3)⋊C311yescharacteristic
111C22×C32C32×D311yescharacteristic
112C2×C3⋊D3—31no—
113C2×C3×D3—93no—
114C2×C3×D3—91no—
115C2×C3×D3—271no—
116C32×C4—271no—
117C3⋊Dic3—31no—
118C3×Dic3—93no—
119C3×Dic3—91no—
120C3×Dic3—271no—
121C22×C9—31no—
122C22×C9—61no—
123C2×D9—91no—
124Dic9—91no—
125C33—31no—
126C33—61no—
127C33C3×#6711yescharacteristic
1283−1+2—31no—
1293−1+2—61no—
130H(3,𝔽3)—23no—
131H(3,𝔽3)—61no—
132H(3,𝔽3)—61no—
133H(3,𝔽3)—61no—
134H(3,𝔽3)C3×#6713yes—
135C3×C9—21no—
136C3×C9C32×D411yescharacteristic, complemented
137C3×D4—271no—
138C3×D4—273no—
139#67—91no—
140#67—271no—
141C2×C32—22no—
142C2×C32—21no—
143C2×C32—21no—
144C2×C32—21no—
145C2×C32—33no—
146C2×C32—63no—
147C2×C32—66no—
148C2×C32—63no—
149C2×C32—91no—
150C2×C32—91no—
151C2×C32—181no—
152C2×C32—181no—
153C2×C32—181no—
154C2×C32—182no—
155C2×C32—186no—
156C2×C32—183no—
157C2×C32—541no—
158C2×C32C2×(C3⋊D3)⋊C311yescharacteristic
159C2×C32C2×C32×D311yescharacteristic
160C3⋊D3—61no—
161C3×D3—183no—
162C3×D3—181no—
163C3×D3—541no—
164C2×C9—31no—
165C2×C9—61no—
166C2×C9—62no—
167C2×C9—61no—
168D9—181no—
169C22×C3—31no—
170C22×C3—31no—
171C22×C3—61no—
172C22×C3—93no—
173C22×C3—183no—
174C22×C3—271no—
175C22×C3—273no—
176C22×C3C3×(C3⋊D3)⋊C311yescharacteristic
177C2×D3—91no—
178C2×D3—271no—
179C3×C4—271no—
180C3×C4—273no—
181Dic3—91no—
182Dic3—271no—
183C32—21no—
184C32—33no—
185C32—63no—
186C32—91no—
187C32—91no—
188C32—181no—
189C32—183no—
190C32#638⋊C311yescharacteristic
191C32C32×#6711yescharacteristic
192C9—31no—
193C9—61no—
194D4—271noSylow
195C2×C3—21no—
196C2×C3—31no—
197C2×C3—31no—
198C2×C3—61no—
199C2×C3—61no—
200C2×C3—62no—
201C2×C3—61no—
202C2×C3—93no—
203C2×C3—183no—
204C2×C3—186no—
205C2×C3—183no—
206C2×C3—541no—
207C2×C3—543no—
208C2×C3C2×C3×(C3⋊D3)⋊C311yescharacteristic
209D3—181no—
210D3—541no—
211C22—271no—
212C22#4179⋊C311yescharacteristic, complemented
213C4—271no—
214C3—31no—
215C3—31no—
216C3—61no—
217C3—93no—
218C3—183no—
219C3C3×#638⋊C311yescharacteristic
220C2—21no—
221C2—541no—
222C2C2×#4179⋊C311yescharacteristic
subgroupG/H
centerC2C2×#4179⋊C3
commutator, cosocleC2×C3×C9C22×C32
FrattiniC2×C32C2×C32×D3
FittingC22×#6911C2
socleC2×C3C2×C3×(C3⋊D3)⋊C3
hypercenterC22#4179⋊C3
hypocenterC3×C9C32×D4
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×#6911C2semidirect
2. C2×#4179⋊C3C2semidirect
3. #66326⋊C3C2semidirect
4. #10619980C3semidirect
6. #10619650C3semidirect
10. C22×C3×3−1+2C2×C3semidirect
13. C2×C3⋊AGL(1,ℤ/9)C2×C3semidirect
15. C3⋊(3−1+2⋊C4)C2×C3semidirect
18. C22×#732C2×C3semidirect
19. C2×#4179C2×C3semidirect
20. #66326C2×C3semidirect
21. #6911D4semidirect
24. #6233C32semidirect
55. C22×C3×C9C2×C32semidirect
56. C2×C3⋊D9C2×C32semidirect
59. C3⋊Dic9C2×C32semidirect
62. C3×3−1+2C3×D4semidirect
66. #732C3×D4semidirect
136. C3×C9C32×D4semidirect
212. C22#4179⋊C3semidirect

Maximal subgroups

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

subgroupindex
C22×#69112
C2×#4179⋊C32
#66326⋊C32
#106199803
C3×#638⋊C33
#106196503