Finite Group Databasebeta

← #14519005

Subgroups — #14519005

Order 1944.

985 conjugacy classes of subgroups; only the 186 normal subgroups are shown.

normal subgroups only

This group has 985 conjugacy classes of subgroups — too many to draw. Only its 186 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×C3×#737C211yesmaximal, characteristic, complemented
2C2×C3⋊#4207C211yesmaximal, characteristic, complemented
3C3⋊#66409C211yesmaximal, characteristic, complemented
4#10619992C311yesmaximal, characteristic, complemented
5#10619983—39nomaximal
6#10619980—32nomaximal
7#10619977—31nomaximal
8C3×#6233—31nomaximal
9C2×C3×#737—21no—
10C2×C3×#737C2211yescharacteristic
11C3⋊#4207—21no—
12C22×#737—29no—
13C22×#737D319yescomplemented
14C22×C3×3−1+2—21no—
15C22×C3×3−1+2—22no—
16C22×C3×3−1+2D312yescomplemented
17C22×C3×H(3,𝔽3)D311yescharacteristic
18C22×C32×C9—21no—
19C22×C32×C9D311yescharacteristic, complemented
20C22×C32×C9C2×C311yescharacteristic, complemented
21C2×C3⋊(C3⋊D9)C2×C311yescharacteristic, complemented
22C2×#4207—39no—
23C2×C3⋊AGL(1,ℤ/9)—32no—
24C2×C3⋊((C3⋊D3)⋊C3)—31no—
25C2×C3×C3⋊D9—31no—
26C3⋊(C3⋊Dic9)C2×C311yescharacteristic, complemented
27#66409—39no—
28C3⋊(3−1+2⋊C4)—32no—
29C3⋊((C3⋊Dic3)⋊C3)—31no—
30C3×C3⋊Dic9—31no—
31C3×#737D411yescharacteristic, complemented, Sylow
32#6312—31no—
33C3×#638—91no—
34#6233—31no—
35#6233—32no—
36#6233—39no—
37#611⋊C3—96no—
38#638⋊C3—93no—
39C3×#611—93no—
40C2×#737—218no—
41C2×#737—29no—
42C2×#737—29no—
43C2×#737C2×D319yes—
44C2×C3×3−1+2—22no—
45C2×C3×3−1+2—24no—
46C2×C3×3−1+2—22no—
47C2×C3×3−1+2—21no—
48C2×C3×3−1+2—22no—
49C2×C3×3−1+2C2×D312yes—
50C2×C3×H(3,𝔽3)—21no—
51C2×C3×H(3,𝔽3)C2×D311yescharacteristic
52C2×C32×C9—22no—
53C2×C32×C9—21no—
54C2×C32×C9—21no—
55C2×C32×C9—21no—
56C2×C32×C9C2×D311yescharacteristic
57C2×C32×C9C22×C311yescharacteristic
58C3⋊(C3⋊D9)—21no—
59#4207—69no—
60C3⋊AGL(1,ℤ/9)—62no—
61C3⋊((C3⋊D3)⋊C3)—61no—
62C3×C3⋊D9—61no—
63C22×C33—21no—
64C22×C33C3×D311yescharacteristic
65C22×C33C3⋊D311yescharacteristic
66C2×C3⋊(C3⋊D3)—31no—
67C2×C3×C3⋊D3—91no—
68C3⋊(C3⋊Dic3)—31no—
69C3×C3⋊Dic3—91no—
70C22×3−1+2—29no—
71C22×3−1+2—218no—
72C22×3−1+2—26no—
73C22×3−1+2C3⋊D316yescomplemented
74C22×H(3,𝔽3)—23no—
75C22×H(3,𝔽3)C3⋊D313yes—
76C22×C3×C9—22no—
77C22×C3×C9—21no—
78C22×C3×C9—29no—
79C22×C3×C9—23no—
80C22×C3×C9C3×D311yescharacteristic
81C22×C3×C9C3×D312yes—
82C22×C3×C9C3×D319yescomplemented
83C22×C3×C9C3⋊D313yescomplemented
84C2×C3⋊D9—31no—
85C2×C3⋊D9—32no—
86C2×C3⋊D9—39no—
87C2×AGL(1,ℤ/9)—96no—
88C2×(C3⋊D3)⋊C3—93no—
89C2×C3×D9—93no—
90C3⋊Dic9—31no—
91C3⋊Dic9—32no—
92C3⋊Dic9—39no—
933−1+2⋊C4—96no—
94(C3⋊Dic3)⋊C3—93no—
95C3×Dic9—93no—
96#737—29no—
97#737#6719yescomplemented
98C3×3−1+2—21no—
99C3×3−1+2—22no—
100C3×3−1+2#6712yescomplemented
101C3×H(3,𝔽3)#6711yescharacteristic
102C32×C9—21no—
103C32×C9#6711yescharacteristic, complemented
104C32×C9C3×D411yescharacteristic, complemented
105#638—91no—
106#638—93no—
107#638—273no—
108C3×#67—273no—
109C3×#67—271no—
110#611—93no—
111#611—96no—
112C2×C33—22no—
113C2×C33—21no—
114C2×C33—21no—
115C2×C33—21no—
116C2×C33C2×C3×D311yescharacteristic
117C2×C33C2×C3⋊D311yescharacteristic
118C3⋊(C3⋊D3)—61no—
119C3×C3⋊D3—181no—
120C2×3−1+2—218no—
121C2×3−1+2—236no—
122C2×3−1+2—212no—
123C2×3−1+2—26no—
124C2×3−1+2—29no—
125C2×3−1+2—218no—
126C2×3−1+2—26no—
127C2×3−1+2C2×C3⋊D316yes—
128C2×H(3,𝔽3)—26no—
129C2×H(3,𝔽3)—23no—
130C2×H(3,𝔽3)—23no—
131C2×H(3,𝔽3)C2×C3⋊D313yes—
132C2×C3×C9—24no—
133C2×C3×C9—22no—
134C2×C3×C9—218no—
135C2×C3×C9—26no—
136C2×C3×C9—21no—
137C2×C3×C9—22no—
138C2×C3×C9—29no—
139C2×C3×C9—23no—
140C2×C3×C9—22no—
141C2×C3×C9—21no—
142C2×C3×C9—29no—
143C2×C3×C9—23no—
144C2×C3×C9C2×C3×D311yescharacteristic
145C2×C3×C9C2×C3×D312yes—
146C2×C3×C9C2×C3×D319yes—
147C2×C3×C9C2×C3⋊D313yes—
148C3⋊D9—61no—
149C3⋊D9—62no—
150C3⋊D9—69no—
151AGL(1,ℤ/9)—186no—
152(C3⋊D3)⋊C3—183no—
153C3×D9—183no—
154C22×C32—21no—
155C22×C32—23no—
156C22×C32—33no—
157C22×C32—33no—
158C22×C32—63no—
159C22×C32C3×C3⋊D313yes—
160C22×C32C3×C3⋊D311yescharacteristic
161C22×C32C3⋊(C3⋊D3)11yescharacteristic
162C2×C3⋊D3—91no—
163C2×C3⋊D3—93no—
164C2×C3⋊D3—273no—
165C2×C3×D3—273no—
166C2×C3×D3—271no—
167C3⋊Dic3—91no—
168C3⋊Dic3—93no—
169C3⋊Dic3—273no—
170C3×Dic3—273no—
171C3×Dic3—271no—
172C22×C9—26no—
173C22×C9—23no—
174C22×C9C3×C3⋊D313yes—
175C22×C9C3×C3⋊D316yes—
176C2×D9—93no—
177C2×D9—96no—
178Dic9—93no—
179Dic9—96no—
180C33—21no—
181C33C3×#6711yescharacteristic
182C33#63811yescharacteristic
1833−1+2—29no—
1843−1+2—218no—
1853−1+2—26no—
1863−1+2#63816yescomplemented
187H(3,𝔽3)—23no—
188H(3,𝔽3)#63813yes—
189C3×C9—22no—
190C3×C9—21no—
191C3×C9—29no—
192C3×C9—23no—
193C3×C9C3×#6711yescharacteristic
194C3×C9C3×#6712yes—
195C3×C9C3×#6719yescomplemented
196C3×C9#63813yescomplemented
197C3×D4—811no—
198#67—273no—
199#67—271no—
200#67—813no—
201C2×C32—21no—
202C2×C32—22no—
203C2×C32—26no—
204C2×C32—23no—
205C2×C32—21no—
206C2×C32—21no—
207C2×C32—23no—
208C2×C32—33no—
209C2×C32—33no—
210C2×C32—63no—
211C2×C32—63no—
212C2×C32—66no—
213C2×C32—63no—
214C2×C32C2×C3×C3⋊D313yes—
215C2×C32C2×C3×C3⋊D311yescharacteristic
216C2×C32C2×C3⋊(C3⋊D3)11yescharacteristic
217C3⋊D3—181no—
218C3⋊D3—183no—
219C3⋊D3—543no—
220C3×D3—543no—
221C3×D3—541no—
222C2×C9—212no—
223C2×C9—26no—
224C2×C9—23no—
225C2×C9—26no—
226C2×C9—26no—
227C2×C9—23no—
228C2×C9C2×C3×C3⋊D313yes—
229C2×C9C2×C3×C3⋊D316yes—
230D9—183no—
231D9—186no—
232C22×C3—33no—
233C22×C3—31no—
234C22×C3—61no—
235C22×C3—63no—
236C22×C3—811no—
237C22×C3#420713yescomplemented
238C22×C3C3×C3⋊(C3⋊D3)11yescharacteristic
239C2×D3—273no—
240C2×D3—271no—
241C2×D3—813no—
242C3×C4—811no—
243Dic3—273no—
244Dic3—271no—
245Dic3—813no—
246C32—21no—
247C32—23no—
248C32—33no—
249C32—33no—
250C32—63no—
251C32C3×#63813yes—
252C32C3×#63811yescharacteristic
253C32#631211yescharacteristic
254C9—26no—
255C9—23no—
256C9C3×#63813yes—
257C9C3×#63816yes—
258D4—811noSylow
259C2×C3—21no—
260C2×C3—23no—
261C2×C3—33no—
262C2×C3—31no—
263C2×C3—63no—
264C2×C3—61no—
265C2×C3—62no—
266C2×C3—66no—
267C2×C3—61no—
268C2×C3—63no—
269C2×C3—1621no—
270C2×C3C2×#420713yes—
271C2×C3C2×C3×C3⋊(C3⋊D3)11yescharacteristic
272D3—541no—
273D3—543no—
274D3—1623no—
275C22—811no—
276C22C3⋊#420711yescharacteristic, complemented
277C4—811no—
278C3—33no—
279C3—31no—
280C3—61no—
281C3—63no—
282C3#1061998313yescomplemented
283C3C3×#631211yescharacteristic
284C2—21no—
285C2—1621no—
286C2C2×C3⋊#420711yescharacteristic
subgroupG/H
centerC2C2×C3⋊#4207
commutator, cosocleC2×C32×C9C22×C3
FrattiniC2×C3C2×C3×C3⋊(C3⋊D3)
FittingC22×C3×#737C2
socleC2×C32C2×C3×C3⋊D3
hypercenterC22C3⋊#4207
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×C3×#737C2semidirect
2. C2×C3⋊#4207C2semidirect
3. C3⋊#66409C2semidirect
4. #10619992C3semidirect
13. C22×#737D3semidirect
16. C22×C3×3−1+2D3semidirect
19. C22×C32×C9D3semidirect
20. C22×C32×C9C2×C3semidirect
21. C2×C3⋊(C3⋊D9)C2×C3semidirect
26. C3⋊(C3⋊Dic9)C2×C3semidirect
31. C3×#737D4semidirect
73. C22×3−1+2C3⋊D3semidirect
82. C22×C3×C9C3×D3semidirect
83. C22×C3×C9C3⋊D3semidirect
97. #737#67semidirect
100. C3×3−1+2#67semidirect
103. C32×C9#67semidirect
104. C32×C9C3×D4semidirect
186. 3−1+2#638semidirect
195. C3×C9C3×#67semidirect
196. C3×C9#638semidirect
237. C22×C3#4207semidirect
276. C22C3⋊#4207semidirect
282. C3#10619983semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#7372
C2×C3⋊#42072
C3⋊#664092
#106199923
#106199833
#106199803
#106199773
C3×#62333