Finite Group Databasebeta

← #14517656

Subgroups — #14517656

Order 1944.

455 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 455 conjugacy classes of subgroups — too many to draw. Only its 75 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×C9⋊H(3,𝔽3)C211yesmaximal, characteristic, complemented
2C2×#92303C211yesmaximal, characteristic, complemented
3#11757607C211yesmaximal, characteristic, complemented
4#10619992C311yesmaximal, characteristic, complemented
5#10619980—31nomaximal
6#10619977—31nomaximal
7#10619630—32nomaximal
8C2×C9⋊H(3,𝔽3)—21no—
9C2×C9⋊H(3,𝔽3)C2211yescharacteristic
10#92303—21no—
11C22×C3×3−1+2—21no—
12C22×C3×3−1+2D311yescharacteristic, complemented
13C22×C3×H(3,𝔽3)D311yescharacteristic
14C22×C32×C9C2×C311yescharacteristic, complemented
15C2×C3⋊(C3⋊D9)C2×C311yescharacteristic, complemented
16C2×C3⋊AGL(1,ℤ/9)—31no—
17C2×C3⋊((C3⋊D3)⋊C3)—31no—
18C3⋊(C3⋊Dic9)C2×C311yescharacteristic, complemented
19C3⋊(3−1+2⋊C4)—31no—
20C3⋊((C3⋊Dic3)⋊C3)—31no—
21C22×C32⋊C9—21no—
22C22×C32⋊C9—22no—
23C22×C32⋊C9D312yescomplemented
24C2×#4169—32no—
25#66316—32no—
26C9⋊H(3,𝔽3)D411yescharacteristic, complemented, Sylow
27#6312—31no—
28C3×#638—91no—
29#6233—31no—
30#6233—32no—
31#6233—93no—
32#611⋊C3—93no—
33#638⋊C3—93no—
34C2×C3×3−1+2—22no—
35C2×C3×3−1+2—21no—
36C2×C3×3−1+2—21no—
37C2×C3×3−1+2C2×D311yescharacteristic
38C2×C3×H(3,𝔽3)—21no—
39C2×C3×H(3,𝔽3)C2×D311yescharacteristic
40C2×C32×C9—21no—
41C2×C32×C9C22×C311yescharacteristic
42C3⋊(C3⋊D9)—21no—
43C3⋊AGL(1,ℤ/9)—61no—
44C3⋊((C3⋊D3)⋊C3)—61no—
45C2×C32⋊C9—22no—
46C2×C32⋊C9—24no—
47C2×C32⋊C9—22no—
48C2×C32⋊C9—21no—
49C2×C32⋊C9—22no—
50C2×C32⋊C9C2×D312yes—
51#4169—62no—
52C22×C33—21no—
53C22×C33C3×D311yescharacteristic
54C22×C33C3⋊D311yescharacteristic
55C2×C3⋊(C3⋊D3)—31no—
56C2×C3×C3⋊D3—91no—
57C3⋊(C3⋊Dic3)—31no—
58C3×C3⋊Dic3—91no—
59C22×3−1+2—33no—
60C22×3−1+2—63no—
61C22×H(3,𝔽3)—33no—
62C22×C3×C9—21no—
63C22×C3×C9—22no—
64C22×C3×C9—33no—
65C22×C3×C9C3×D312yes—
66C22×C3×C9C3×D311yescharacteristic
67C2×C3⋊D9—31no—
68C2×C3⋊D9—32no—
69C2×C3⋊D9—93no—
70C2×AGL(1,ℤ/9)—93no—
71C2×(C3⋊D3)⋊C3—93no—
72C3⋊Dic9—31no—
73C3⋊Dic9—32no—
74C3⋊Dic9—93no—
753−1+2⋊C4—93no—
76(C3⋊Dic3)⋊C3—93no—
77C3×3−1+2—21no—
78C3×3−1+2#6711yescharacteristic, complemented
79C3×H(3,𝔽3)#6711yescharacteristic
80C32×C9C3×D411yescharacteristic, complemented
81C32⋊C9—21no—
82C32⋊C9—22no—
83C32⋊C9#6712yescomplemented
84#638—91no—
85#638—93no—
86#638—271no—
87#638—272no—
88C3×#67—271no—
89C3×#67—271no—
90C3×#67—272no—
91#611—93no—
92#611—272no—
93C2×C33—21no—
94C2×C33—22no—
95C2×C33—21no—
96C2×C33—21no—
97C2×C33C2×C3×D311yescharacteristic
98C2×C33C2×C3⋊D311yescharacteristic
99C3⋊(C3⋊D3)—61no—
100C3×C3⋊D3—181no—
101C2×3−1+2—33no—
102C2×3−1+2—63no—
103C2×3−1+2—66no—
104C2×3−1+2—63no—
105C2×H(3,𝔽3)—33no—
106C2×H(3,𝔽3)—63no—
107C2×C3×C9—21no—
108C2×C3×C9—22no—
109C2×C3×C9—24no—
110C2×C3×C9—22no—
111C2×C3×C9—21no—
112C2×C3×C9—22no—
113C2×C3×C9—33no—
114C2×C3×C9—63no—
115C2×C3×C9C2×C3×D312yes—
116C2×C3×C9C2×C3×D311yescharacteristic
117C3⋊D9—61no—
118C3⋊D9—62no—
119C3⋊D9—183no—
120AGL(1,ℤ/9)—183no—
121(C3⋊D3)⋊C3—183no—
122C22×C32—31no—
123C22×C32—32no—
124C22×C32—31no—
125C22×C32—31no—
126C22×C32—32no—
127C22×C32—61no—
128C22×C32—61no—
129C22×C32—62no—
130C22×C32AGL(1,ℤ/9)13yescomplemented
131C22×C32C3×C3⋊D311yescharacteristic
132C2×C3⋊D3—91no—
133C2×C3⋊D3—93no—
134C2×C3⋊D3—271no—
135C2×C3⋊D3—272no—
136C2×C3×D3—271no—
137C2×C3×D3—271no—
138C2×C3×D3—272no—
139C3⋊Dic3—91no—
140C3⋊Dic3—93no—
141C3⋊Dic3—271no—
142C3⋊Dic3—272no—
143C3×Dic3—271no—
144C3×Dic3—271no—
145C3×Dic3—272no—
146C22×C9—32no—
147C22×C9—61no—
148C22×C9—62no—
149C22×C9(C3⋊D3)⋊C313yescomplemented
150C2×D9—93no—
151C2×D9—272no—
152Dic9—93no—
153Dic9—272no—
154C33—21no—
155C33C3×#6711yescharacteristic
156C33#63811yescharacteristic
1573−1+2—33no—
1583−1+2—63no—
159H(3,𝔽3)—33no—
160C3×C9—21no—
161C3×C9—22no—
162C3×C9—33no—
163C3×C9C3×#6712yes—
164C3×C9C3×#6711yescharacteristic
165C3×D4—811no—
166#67—271no—
167#67—271no—
168#67—272no—
169#67—813no—
170C2×C32—21no—
171C2×C32—23no—
172C2×C32—31no—
173C2×C32—32no—
174C2×C32—31no—
175C2×C32—31no—
176C2×C32—32no—
177C2×C32—61no—
178C2×C32—62no—
179C2×C32—61no—
180C2×C32—61no—
181C2×C32—62no—
182C2×C32—62no—
183C2×C32—62no—
184C2×C32—64no—
185C2×C32—61no—
186C2×C32—61no—
187C2×C32—62no—
188C2×C32C2×AGL(1,ℤ/9)13yes—
189C2×C32C2×C3×C3⋊D311yescharacteristic
190C3⋊D3—181no—
191C3⋊D3—183no—
192C3⋊D3—541no—
193C3⋊D3—542no—
194C3×D3—541no—
195C3×D3—541no—
196C3×D3—542no—
197C2×C9—23no—
198C2×C9—32no—
199C2×C9—62no—
200C2×C9—62no—
201C2×C9—64no—
202C2×C9—61no—
203C2×C9—62no—
204C2×C9C2×(C3⋊D3)⋊C313yes—
205D9—183no—
206D9—542no—
207C22×C3—33no—
208C22×C3—91no—
209C22×C3—181no—
210C22×C3—811no—
211C22×C3C3⋊((C3⋊D3)⋊C3)11yescharacteristic
212C22×C3C3⋊AGL(1,ℤ/9)11yescharacteristic
213C22×C3#420712yes—
214C2×D3—271no—
215C2×D3—271no—
216C2×D3—272no—
217C2×D3—813no—
218C3×C4—811no—
219Dic3—271no—
220Dic3—271no—
221Dic3—272no—
222Dic3—813no—
223C32—31no—
224C32—32no—
225C32—31no—
226C32—31no—
227C32—32no—
228C32—61no—
229C32—61no—
230C32—62no—
231C32#611⋊C313yescomplemented
232C32C3×#63811yescharacteristic
233C9—32no—
234C9—61no—
235C9—62no—
236C9#638⋊C313yescomplemented
237D4—811noSylow
238C2×C3—21no—
239C2×C3—21no—
240C2×C3—22no—
241C2×C3—33no—
242C2×C3—63no—
243C2×C3—91no—
244C2×C3—181no—
245C2×C3—182no—
246C2×C3—181no—
247C2×C3—1621no—
248C2×C3C2×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
249C2×C3C2×C3⋊AGL(1,ℤ/9)11yescharacteristic
250C2×C3C2×#420712yes—
251D3—541no—
252D3—541no—
253D3—542no—
254D3—1623no—
255C22—811no—
256C22#9230311yescharacteristic, complemented
257C4—811no—
258C3—33no—
259C3—91no—
260C3—181no—
261C3#1061997711yescharacteristic
262C3#1061998011yescharacteristic
263C3#1061998312yes—
264C2—21no—
265C2—1621no—
266C2C2×#9230311yescharacteristic
subgroupG/H
centerC2C2×#92303
commutator, cosocleC2×C32×C9C22×C3
Frattini, socleC2×C32C2×C3×C3⋊D3
FittingC22×C9⋊H(3,𝔽3)C2
hypercenterC22#92303
hypocenterC32×C9C3×D4
LCSG ▷ C2×C32×C9 ▷ C32×C9
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C9⋊H(3,𝔽3)C2semidirect
2. C2×#92303C2semidirect
3. #11757607C2semidirect
4. #10619992C3semidirect
12. C22×C3×3−1+2D3semidirect
14. C22×C32×C9C2×C3semidirect
15. C2×C3⋊(C3⋊D9)C2×C3semidirect
18. C3⋊(C3⋊Dic9)C2×C3semidirect
23. C22×C32⋊C9D3semidirect
26. C9⋊H(3,𝔽3)D4semidirect
78. C3×3−1+2#67semidirect
80. C32×C9C3×D4semidirect
83. C32⋊C9#67semidirect
130. C22×C32AGL(1,ℤ/9)semidirect
149. C22×C9(C3⋊D3)⋊C3semidirect
231. C32#611⋊C3semidirect
236. C9#638⋊C3semidirect
256. C22#92303semidirect

Maximal subgroups

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

subgroupindex
C22×C9⋊H(3,𝔽3)2
C2×#923032
#117576072
#106199923
#106199803
#106199773
#106196303