Finite Group Databasebeta

← #14517710

Subgroups — #14517710

Order 1944.

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

normal subgroups only

This group has 360 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×#6908C211yesmaximal, characteristic, complemented
2C2×#92330C211yesmaximal, characteristic, complemented
3#11757634C211yesmaximal, characteristic, complemented
4#10619992C311yesmaximal, characteristic, complemented
5#10619983—31nomaximal
6#10619650—31nomaximal
7#10619646—31nomaximal
8#10619642—31nomaximal
9C2×#6908—21no—
10C2×#6908C2211yescharacteristic
11#92330—21no—
12C22×#737—21no—
13C22×#737D311yescharacteristic, complemented
14C22×C32×C9C2×C311yescharacteristic, complemented
15C2×C3⋊(C3⋊D9)C2×C311yescharacteristic, complemented
16C2×#4207—31no—
17C3⋊(C3⋊Dic9)C2×C311yescharacteristic, complemented
18#66409—31no—
19C22×#733—21no—
20C22×#732D311yescharacteristic, complemented
21C22×#731—21no—
22C22×#731D311yescharacteristic, complemented
23C22×AΣL(1,𝔽27)—21no—
24C22×AΣL(1,𝔽27)D311yescharacteristic
25C2×#4179—31no—
26C2×#4177—31no—
27C2×#4175—31no—
28#66326—31no—
29#66324—31no—
30#66322—31no—
31#6908D411yescharacteristic, complemented, Sylow
32#6312—31no—
33#6233—31no—
34#6233—31no—
35#6233—31no—
36#6233—91no—
37#6233—92no—
38#611⋊C3—92no—
39#638⋊C3—91no—
40C3×#611—91no—
41C2×#737—22no—
42C2×#737—21no—
43C2×#737—21no—
44C2×#737C2×D311yescharacteristic
45C2×C32×C9—21no—
46C2×C32×C9C22×C311yescharacteristic
47C3⋊(C3⋊D9)—21no—
48#4207—61no—
49C2×#733—22no—
50C2×#733—21no—
51C2×#732—21no—
52C2×#732C2×D311yescharacteristic
53C2×#731—22no—
54C2×#731—21no—
55C2×#731—21no—
56C2×#731C2×D311yescharacteristic
57C2×AΣL(1,𝔽27)—22no—
58C2×AΣL(1,𝔽27)—21no—
59C2×AΣL(1,𝔽27)—21no—
60C2×AΣL(1,𝔽27)C2×D311yescharacteristic
61#4179—61no—
62#4177—61no—
63#4175—61no—
64C22×C33C3×D311yescharacteristic
65C2×C3⋊(C3⋊D3)—31no—
66C3⋊(C3⋊Dic3)—31no—
67C22×3−1+2—21no—
68C22×3−1+2—21no—
69C22×3−1+2—21no—
70C22×3−1+2—32no—
71C22×3−1+2—62no—
72C22×H(3,𝔽3)—21no—
73C22×H(3,𝔽3)C3⋊D311yescharacteristic
74C22×C3×C9—31no—
75C22×C3×C9—32no—
76C22×C3×C9—31no—
77C22×C3×C9—61no—
78C22×C3×C9C3×D311yescharacteristic
79C22×C3×C9C3×D311yescharacteristic
80C22×C3×C9C3×D311yescharacteristic
81C2×C3⋊D9—31no—
82C2×C3⋊D9—31no—
83C2×C3⋊D9—31no—
84C2×C3⋊D9—91no—
85C2×C3⋊D9—92no—
86C2×AGL(1,ℤ/9)—92no—
87C2×(C3⋊D3)⋊C3—91no—
88C2×C3×D9—91no—
89C3⋊Dic9—31no—
90C3⋊Dic9—31no—
91C3⋊Dic9—31no—
92C3⋊Dic9—91no—
93C3⋊Dic9—92no—
943−1+2⋊C4—92no—
95(C3⋊Dic3)⋊C3—91no—
96C3×Dic9—91no—
97#737—21no—
98#737#6711yescharacteristic, complemented
99C32×C9C3×D411yescharacteristic, complemented
100#733—21no—
101#732#6711yescharacteristic, complemented
102#731—21no—
103#731#6711yescharacteristic, complemented
104AΣL(1,𝔽27)—21no—
105AΣL(1,𝔽27)#6711yescharacteristic
106#638—91no—
107#638—271no—
108#638—273no—
109C3×#67—271no—
110#611—91no—
111#611—92no—
112#611—271no—
113#611—271no—
114C2×C33—21no—
115C2×C33C2×C3×D311yescharacteristic
116C3⋊(C3⋊D3)—61no—
117C2×3−1+2—22no—
118C2×3−1+2—22no—
119C2×3−1+2—22no—
120C2×3−1+2—21no—
121C2×3−1+2—21no—
122C2×3−1+2—21no—
123C2×3−1+2—32no—
124C2×3−1+2—62no—
125C2×3−1+2—64no—
126C2×3−1+2—62no—
127C2×H(3,𝔽3)—22no—
128C2×H(3,𝔽3)—21no—
129C2×H(3,𝔽3)—21no—
130C2×H(3,𝔽3)C2×C3⋊D311yescharacteristic
131C2×C3×C9—21no—
132C2×C3×C9—21no—
133C2×C3×C9—21no—
134C2×C3×C9—31no—
135C2×C3×C9—32no—
136C2×C3×C9—31no—
137C2×C3×C9—61no—
138C2×C3×C9—62no—
139C2×C3×C9—61no—
140C2×C3×C9—62no—
141C2×C3×C9—61no—
142C2×C3×C9C2×C3×D311yescharacteristic
143C2×C3×C9C2×C3×D311yescharacteristic
144C2×C3×C9C2×C3×D311yescharacteristic
145C3⋊D9—61no—
146C3⋊D9—61no—
147C3⋊D9—61no—
148C3⋊D9—181no—
149C3⋊D9—182no—
150AGL(1,ℤ/9)—182no—
151(C3⋊D3)⋊C3—181no—
152C3×D9—181no—
153C22×C32—31no—
154C22×C32—33no—
155C22×C32—31no—
156C22×C32—61no—
157C22×C32C3×C3⋊D311yescharacteristic
158C2×C3⋊D3—91no—
159C2×C3⋊D3—271no—
160C2×C3⋊D3—273no—
161C2×C3×D3—271no—
162C3⋊Dic3—91no—
163C3⋊Dic3—271no—
164C3⋊Dic3—273no—
165C3×Dic3—271no—
166C22×C9—31no—
167C22×C9—31no—
168C22×C9—61no—
169C22×C9—61no—
170C22×C9—61no—
171C22×C9(C3⋊D3)⋊C311yescharacteristic
172C22×C9(C3⋊D3)⋊C312yes—
173C2×D9—91no—
174C2×D9—92no—
175C2×D9—271no—
176C2×D9—271no—
177Dic9—91no—
178Dic9—92no—
179Dic9—271no—
180Dic9—271no—
181C33C3×#6711yescharacteristic
1823−1+2—21no—
1833−1+2—21no—
1843−1+2—21no—
1853−1+2—32no—
1863−1+2—62no—
187H(3,𝔽3)—21no—
188H(3,𝔽3)#63811yescharacteristic
189C3×C9—31no—
190C3×C9—32no—
191C3×C9—31no—
192C3×C9—61no—
193C3×C9C3×#6711yescharacteristic
194C3×C9C3×#6711yescharacteristic
195C3×C9C3×#6711yescharacteristic
196C3×D4—811no—
197#67—271no—
198#67—811no—
199#67—813no—
200C2×C32—21no—
201C2×C32—31no—
202C2×C32—33no—
203C2×C32—31no—
204C2×C32—61no—
205C2×C32—61no—
206C2×C32—62no—
207C2×C32—63no—
208C2×C32—61no—
209C2×C32C2×C3×C3⋊D311yescharacteristic
210C3⋊D3—181no—
211C3⋊D3—541no—
212C3⋊D3—543no—
213C3×D3—541no—
214C2×C9—21no—
215C2×C9—22no—
216C2×C9—31no—
217C2×C9—31no—
218C2×C9—61no—
219C2×C9—61no—
220C2×C9—62no—
221C2×C9—62no—
222C2×C9—62no—
223C2×C9—61no—
224C2×C9—61no—
225C2×C9—61no—
226C2×C9C2×(C3⋊D3)⋊C311yescharacteristic
227C2×C9C2×(C3⋊D3)⋊C312yes—
228D9—181no—
229D9—182no—
230D9—541no—
231D9—541no—
232C22×C3—33no—
233C22×C3—31no—
234C22×C3—91no—
235C22×C3—181no—
236C22×C3—811no—
237C22×C3C3⋊((C3⋊D3)⋊C3)11yescharacteristic
238C2×D3—271no—
239C2×D3—811no—
240C2×D3—813no—
241C3×C4—811no—
242Dic3—271no—
243Dic3—811no—
244Dic3—813no—
245C32—33no—
246C32—31no—
247C32—31no—
248C32—61no—
249C32C3×#63811yescharacteristic
250C9—31no—
251C9—31no—
252C9—61no—
253C9—61no—
254C9—61no—
255C9#638⋊C311yescharacteristic
256C9#638⋊C312yes—
257D4—811noSylow
258C2×C3—21no—
259C2×C3—33no—
260C2×C3—31no—
261C2×C3—61no—
262C2×C3—63no—
263C2×C3—91no—
264C2×C3—181no—
265C2×C3—182no—
266C2×C3—181no—
267C2×C3—1621no—
268C2×C3C2×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
269D3—541no—
270D3—1621no—
271D3—1623no—
272C22—811no—
273C22#9233011yescharacteristic, complemented
274C4—811no—
275C3—33no—
276C3—31no—
277C3—91no—
278C3—181no—
279C3#1061997711yescharacteristic
280C2—21no—
281C2—1621no—
282C2C2×#9233011yescharacteristic
subgroupG/H
centerC2C2×#92330
commutator, cosocleC2×C32×C9C22×C3
FrattiniC2×C32C2×C3×C3⋊D3
FittingC22×#6908C2
socleC2×C3C2×C3⋊((C3⋊D3)⋊C3)
hypercenterC22#92330
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×#6908C2semidirect
2. C2×#92330C2semidirect
3. #11757634C2semidirect
4. #10619992C3semidirect
13. C22×#737D3semidirect
14. C22×C32×C9C2×C3semidirect
15. C2×C3⋊(C3⋊D9)C2×C3semidirect
17. C3⋊(C3⋊Dic9)C2×C3semidirect
20. C22×#732D3semidirect
22. C22×#731D3semidirect
31. #6908D4semidirect
98. #737#67semidirect
99. C32×C9C3×D4semidirect
101. #732#67semidirect
103. #731#67semidirect
273. C22#92330semidirect

Maximal subgroups

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

subgroupindex
C22×#69082
C2×#923302
#117576342
#106199923
#106199833
#106196503
#106196463
#106196423