Finite Group Databasebeta

← #10619681⋊C3 #14517714

Subgroups — #10619681⋊C3 #14517714

Order 1944.

390 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 57 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, complemented
2C2×#4184⋊C3C211yesmaximal, characteristic, complemented
3#66331⋊C3C211yesmaximal, characteristic, complemented
4C3×#611⋊C3—32nomaximal
5C3×#611⋊C3—31nomaximal
6C3×#638⋊C3—31nomaximal
7#10619681C311yesmaximal, characteristic, complemented
8C2×#6910—21no—
9C2×#6910C2211yescharacteristic
10#4184⋊C3—21no—
11C22×C3×3−1+2D311yescharacteristic, complemented
12C22×C3×3−1+2D312yescomplemented
13C22×C3×H(3,𝔽3)D311yescharacteristic
14C2×C3×AGL(1,ℤ/9)—32no—
15C2×C3×AGL(1,ℤ/9)—31no—
16C2×C3×(C3⋊D3)⋊C3—31no—
17C3×3−1+2⋊C4—32no—
18C3×3−1+2⋊C4—31no—
19C3×(C3⋊Dic3)⋊C3—31no—
20C22×#731—22no—
21C22×#731—21no—
22C22×#731—21no—
23C22×#731C2×C311yescharacteristic, complemented
24C2×#4184C2×C311yescharacteristic, complemented
25#66331C2×C311yescharacteristic, complemented
26#6910D411yescharacteristic, complemented, Sylow
27C3×#638—31no—
28C32×#67—91no—
29#611⋊C3—32no—
30#611⋊C3—32no—
31#611⋊C3—32no—
32#611⋊C3—31no—
33#611⋊C3—32no—
34#638⋊C3—32no—
35#638⋊C3—31no—
36C3×#611—32no—
37C3×#611—31no—
38C2×C3×3−1+2—21no—
39C2×C3×3−1+2—22no—
40C2×C3×3−1+2C2×D311yescharacteristic
41C2×C3×3−1+2C2×D312yes—
42C2×C3×H(3,𝔽3)—21no—
43C2×C3×H(3,𝔽3)C2×D311yescharacteristic
44C3×AGL(1,ℤ/9)—62no—
45C3×AGL(1,ℤ/9)—61no—
46C3×(C3⋊D3)⋊C3—61no—
47C2×#731—24no—
48C2×#731—22no—
49C2×#731—22no—
50C2×#731—21no—
51C2×#731—22no—
52C2×#731—21no—
53C2×#731—21no—
54C2×#731C22×C311yescharacteristic
55#4184—21no—
56C22×C33—31no—
57C22×C33C3⋊D311yescharacteristic
58C2×C3×C3⋊D3—31no—
59C2×C32×D3—91no—
60C3×C3⋊Dic3—31no—
61C32×Dic3—91no—
62C22×3−1+2—22no—
63C22×3−1+2—32no—
64C22×3−1+2—32no—
65C22×3−1+2—32no—
66C22×3−1+2—31no—
67C22×3−1+2C3×D312yescomplemented
68C22×H(3,𝔽3)—21no—
69C22×H(3,𝔽3)—32no—
70C22×H(3,𝔽3)C3×D311yescharacteristic
71C22×C3×C9—21no—
72C22×C3×C9—32no—
73C22×C3×C9C3×D311yescharacteristic, complemented
74C2×AGL(1,ℤ/9)—32no—
75C2×AGL(1,ℤ/9)—32no—
76C2×AGL(1,ℤ/9)—32no—
77C2×AGL(1,ℤ/9)—31no—
78C2×AGL(1,ℤ/9)—32no—
79C2×(C3⋊D3)⋊C3—32no—
80C2×(C3⋊D3)⋊C3—31no—
81C2×C3×D9—32no—
82C2×C3×D9—31no—
833−1+2⋊C4—32no—
843−1+2⋊C4—32no—
853−1+2⋊C4—32no—
863−1+2⋊C4—31no—
873−1+2⋊C4—32no—
88(C3⋊Dic3)⋊C3—32no—
89(C3⋊Dic3)⋊C3—31no—
90C3×Dic9—32no—
91C3×Dic9—31no—
92C3×3−1+2#6711yescharacteristic, complemented
93C3×3−1+2#6712yescomplemented
94C3×H(3,𝔽3)#6711yescharacteristic
95#731—22no—
96#731—21no—
97#731—21no—
98#731C3×D411yescharacteristic, complemented
99C32×D4—271no—
100#638—31no—
101C3×#67—92no—
102C3×#67—91no—
103C3×#67—91no—
104C3×#67—271no—
105#611—32no—
106#611—31no—
107C2×C33—21no—
108C2×C33—31no—
109C2×C33—61no—
110C2×C33C2×C3⋊D311yescharacteristic
111C3×C3⋊D3—61no—
112C32×D3—181no—
113C2×3−1+2—24no—
114C2×3−1+2—22no—
115C2×3−1+2—22no—
116C2×3−1+2—32no—
117C2×3−1+2—32no—
118C2×3−1+2—32no—
119C2×3−1+2—31no—
120C2×3−1+2—62no—
121C2×3−1+2—61no—
122C2×3−1+2—62no—
123C2×3−1+2—62no—
124C2×3−1+2C2×C3×D312yes—
125C2×H(3,𝔽3)—22no—
126C2×H(3,𝔽3)—21no—
127C2×H(3,𝔽3)—21no—
128C2×H(3,𝔽3)—32no—
129C2×H(3,𝔽3)—62no—
130C2×H(3,𝔽3)C2×C3×D311yescharacteristic
131C2×C3×C9—22no—
132C2×C3×C9—21no—
133C2×C3×C9—21no—
134C2×C3×C9—32no—
135C2×C3×C9—62no—
136C2×C3×C9C2×C3×D311yescharacteristic
137AGL(1,ℤ/9)—62no—
138AGL(1,ℤ/9)—62no—
139AGL(1,ℤ/9)—62no—
140AGL(1,ℤ/9)—61no—
141AGL(1,ℤ/9)—62no—
142(C3⋊D3)⋊C3—62no—
143(C3⋊D3)⋊C3—61no—
144C3×D9—62no—
145C3×D9—61no—
146C22×C32—31no—
147C22×C32—61no—
148C22×C32—91no—
149C22×C32—91no—
150C22×C32—181no—
151C22×C32—271no—
152C22×C32#27212yes—
153C22×C32#27211yescharacteristic
154C22×C32C3×C3⋊D311yescharacteristic
155C2×C3⋊D3—31no—
156C2×C3×D3—92no—
157C2×C3×D3—91no—
158C2×C3×D3—91no—
159C2×C3×D3—271no—
160C32×C4—271no—
161C3⋊Dic3—31no—
162C3×Dic3—92no—
163C3×Dic3—91no—
164C3×Dic3—91no—
165C3×Dic3—271no—
166C22×C9—32no—
167C22×C9—31no—
168C22×C9—61no—
169C22×C9—62no—
170C2×D9—32no—
171C2×D9—31no—
172Dic9—32no—
173Dic9—31no—
174C33—31no—
175C33#63811yescharacteristic
1763−1+2—22no—
1773−1+2—32no—
1783−1+2—32no—
1793−1+2—32no—
1803−1+2—31no—
1813−1+2C3×#6712yescomplemented
182H(3,𝔽3)—21no—
183H(3,𝔽3)—32no—
184H(3,𝔽3)C3×#6711yescharacteristic
185C3×C9—21no—
186C3×C9—32no—
187C3×C9C3×#6711yescharacteristic, complemented
188C3×D4—271no—
189C3×D4—272no—
190C3×D4—271no—
191#67—91no—
192#67—271no—
193C2×C32—22no—
194C2×C32—21no—
195C2×C32—21no—
196C2×C32—31no—
197C2×C32—61no—
198C2×C32—62no—
199C2×C32—61no—
200C2×C32—91no—
201C2×C32—91no—
202C2×C32—181no—
203C2×C32—181no—
204C2×C32—181no—
205C2×C32—182no—
206C2×C32—541no—
207C2×C32C2×#27212yes—
208C2×C32C2×#27211yescharacteristic
209C2×C32C2×C3×C3⋊D311yescharacteristic
210C3⋊D3—61no—
211C3×D3—182no—
212C3×D3—181no—
213C3×D3—181no—
214C3×D3—541no—
215C2×C9—32no—
216C2×C9—31no—
217C2×C9—61no—
218C2×C9—62no—
219C2×C9—62no—
220C2×C9—64no—
221C2×C9—61no—
222C2×C9—62no—
223D9—62no—
224D9—61no—
225C22×C3—31no—
226C22×C3—32no—
227C22×C3—31no—
228C22×C3—91no—
229C22×C3—181no—
230C22×C3—271no—
231C22×C3—272no—
232C22×C3—271no—
233C22×C3C3×#27211yescharacteristic
234C2×D3—91no—
235C2×D3—271no—
236C3×C4—271no—
237C3×C4—272no—
238C3×C4—271no—
239Dic3—91no—
240Dic3—271no—
241C32—31no—
242C32—61no—
243C32—91no—
244C32—91no—
245C32—181no—
246C32#623512yes—
247C32#623511yescharacteristic
248C32C3×#63811yescharacteristic
249C9—32no—
250C9—31no—
251C9—61no—
252C9—62no—
253D4—271noSylow
254C2×C3—21no—
255C2×C3—31no—
256C2×C3—32no—
257C2×C3—31no—
258C2×C3—62no—
259C2×C3—61no—
260C2×C3—61no—
261C2×C3—91no—
262C2×C3—181no—
263C2×C3—182no—
264C2×C3—181no—
265C2×C3—541no—
266C2×C3—542no—
267C2×C3—541no—
268C2×C3C2×C3×#27211yescharacteristic
269D3—181no—
270D3—541no—
271C22—271no—
272C22#4184⋊C311yescharacteristic, complemented
273C4—271no—
274C3—31no—
275C3—32no—
276C3—31no—
277C3—91no—
278C3—181no—
279C3C3×#623511yescharacteristic
280C2—21no—
281C2—541no—
282C2C2×#4184⋊C311yescharacteristic
subgroupG/H
centerC2C2×#4184⋊C3
commutator, cosocleC2×#731C22×C3
FrattiniC2×C32C2×C3×C3⋊D3
FittingC22×#6910C2
socleC2×C3C2×C3×#272
hypercenterC22#4184⋊C3
hypocenter#731C3×D4
LCSG ▷ C2×#731 ▷ #731
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×#6910C2semidirect
2. C2×#4184⋊C3C2semidirect
3. #66331⋊C3C2semidirect
7. #10619681C3semidirect
11. C22×C3×3−1+2D3semidirect
12. C22×C3×3−1+2D3semidirect
23. C22×#731C2×C3semidirect
24. C2×#4184C2×C3semidirect
25. #66331C2×C3semidirect
26. #6910D4semidirect
67. C22×3−1+2C3×D3semidirect
73. C22×C3×C9C3×D3semidirect
92. C3×3−1+2#67semidirect
93. C3×3−1+2#67semidirect
98. #731C3×D4semidirect
181. 3−1+2C3×#67semidirect
187. C3×C9C3×#67semidirect
272. C22#4184⋊C3semidirect

Maximal subgroups

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

subgroupindex
C22×#69102
C2×#4184⋊C32
#66331⋊C32
C3×#611⋊C33
C3×#638⋊C33
#106196813