Finite Group Databasebeta

← D3×#66366 #14518209

Subgroups — D3×#66366 #14518209

Order 1944.

321 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 321 conjugacy classes of subgroups — too many to draw. Only its 36 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
1C3×#66366C211yesmaximal, characteristic, complemented
2C32×D3×A4C311yesmaximal, characteristic, complemented
3C22×D3×3−1+2C311yesmaximal, characteristic, complemented
4D3×C22⋊H(3,𝔽3)C311yesmaximal, characteristic, complemented
5D3×#1094C311yesmaximal, characteristic, complemented
6C2×#66366—31nomaximal
7D3×AΣL(1,𝔽27)—41nomaximal
8C33×A4C2×C311yescharacteristic, complemented
9C22×C3×3−1+2C2×C311yescharacteristic, complemented
10C2×D3×3−1+2—31no—
11C2×D3×3−1+2—31no—
12C3×C22⋊H(3,𝔽3)C2×C311yescharacteristic, complemented
13C3×#1094C2×C311yescharacteristic, complemented
14#66366—21no—
15#66366—21no—
16#66366—21no—
17#66366—21no—
18#66366D311yescharacteristic, direct product factor
19C3×AΣL(1,𝔽27)—41noSylow
20C22×C32×D3C3211yescharacteristic
21C2×C32×A4—31no—
22C3×D3×A4—31no—
23C3×D3×A4—33no—
24C3×D3×A4—31no—
25C23×3−1+2—31no—
26C22×D3×C9—31no—
27C2×C22⋊H(3,𝔽3)—31no—
28C2×#1094—31no—
29D3×C22⋊C9—31no—
30C33×D3—41no—
31C2×C3×3−1+2—31no—
32D3×3−1+2—31no—
33D3×3−1+2—41no—
34D3×3−1+2A411yescharacteristic, complemented
35D3×H(3,𝔽3)—41no—
36C2×AΣL(1,𝔽27)—121no—
37C22×C33C2×C3211yescharacteristic
38C2×C32×D3—31no—
39C2×C32×D3—31no—
40C32×A4—21no—
41C32×A4—31no—
42C32×A4—33no—
43C32×A4—31no—
44C32×A4—61no—
45C32×A4—63no—
46C32×A4C3×D311yescharacteristic, complemented
47C22×3−1+2—21no—
48C22×3−1+2—61no—
49C22×3−1+2—91no—
50C22×3−1+2—91no—
51C22×3−1+2C3×D311yescharacteristic, complemented
52C22×C3×C9—31no—
53C2×D3×C9—33no—
54C2×D3×C9—33no—
55C22⋊H(3,𝔽3)—21no—
56C22⋊H(3,𝔽3)—61no—
57C22⋊H(3,𝔽3)C3×D311yescharacteristic, complemented
58#1094—21no—
59#1094—61no—
60#1094C3×D311yescharacteristic, complemented
61C3×C22⋊C9—31no—
62C34—41no—
63C3×3−1+2—41no—
64C3×3−1+2C2×A411yescharacteristic, complemented
65C3×H(3,𝔽3)—41no—
66AΣL(1,𝔽27)—41no—
67AΣL(1,𝔽27)—81no—
68AΣL(1,𝔽27)—81no—
69AΣL(1,𝔽27)—81no—
70AΣL(1,𝔽27)—81no—
71C23×C32—31no—
72C22×C3×D3—31no—
73C22×C3×D3H(3,𝔽3)11yescharacteristic
74C2×C3×A4—91no—
75C2×C3×A4—93no—
76C2×C3×A4—91no—
77D3×A4—33no—
78D3×A4—91no—
79C23×C9—91no—
80C2×C22⋊C9—91no—
81C2×C33—31no—
82C2×C33—121no—
83C32×D3—31no—
84C32×D3—123no—
85C32×D3—121no—
86C32×D3—121no—
87C32×D3C3×A411yescharacteristic
88C2×3−1+2—31no—
89C2×3−1+2—31no—
90C2×3−1+2—63no—
91C2×3−1+2—61no—
92C2×3−1+2—91no—
93C2×3−1+2—121no—
94C2×H(3,𝔽3)—121no—
95C2×C3×C9—33no—
96D3×C9—33no—
97D3×C9—31no—
98D3×C9—121no—
99C22×C32—21no—
100C22×C32—31no—
101C22×C32—61no—
102C22×C32—91no—
103C22×C32—91no—
104C22×C32C2×H(3,𝔽3)11yescharacteristic
105C22×C32C32×D311yescharacteristic
106C2×C3×D3—31no—
107C2×C3×D3—31no—
108C2×C3×D3—91no—
109C2×C3×D3—91no—
110C3×A4—31no—
111C3×A4—33no—
112C3×A4—33no—
113C3×A4—31no—
114C3×A4—63no—
115C3×A4—66no—
116C3×A4—63no—
117C3×A4—61no—
118C3×A4—63no—
119C3×A4—61no—
120C3×A4—91no—
121C3×A4—181no—
122C22×C9—31no—
123C22×C9—61no—
124C22×C9—93no—
125C22×C9—93no—
126C22⋊C9—31no—
127C22⋊C9—61no—
128C33—41no—
129C33—81no—
130C33—123no—
131C33—121no—
132C33—121no—
133C33—241no—
134C33—243no—
135C33C2×C3×A411yescharacteristic
1363−1+2—21no—
1373−1+2—41no—
1383−1+2—61no—
1393−1+2—81no—
1403−1+2—241no—
1413−1+2D3×A411yescharacteristic, complemented
142H(3,𝔽3)—41no—
143H(3,𝔽3)—81no—
144H(3,𝔽3)—241no—
145C3×C9—31no—
146C3×C9—121no—
147C23×C3—31no—
148C23×C3—91no—
149C22×D3AΣL(1,𝔽27)11yescharacteristic, complemented
150C2×A4—93no—
151C2×A4—271no—
152C2×C32—31no—
153C2×C32—31no—
154C2×C32—31no—
155C2×C32—61no—
156C2×C32—91no—
157C2×C32—91no—
158C2×C32—181no—
159C2×C32—361no—
160C2×C32—361no—
161C2×C32—363no—
162C3×D3—31no—
163C3×D3—31no—
164C3×D3—91no—
165C3×D3—123no—
166C3×D3—361no—
167C3×D3C22⋊H(3,𝔽3)11yescharacteristic
168C2×C9—33no—
169C2×C9—63no—
170C2×C9—91no—
171C2×C9—93no—
172C2×C9—361no—
173C22×C3—21no—
174C22×C3—31no—
175C22×C3—61no—
176C22×C3—91no—
177C22×C3—91no—
178C22×C3—271no—
179C22×C3—271no—
180C22×C3C2×AΣL(1,𝔽27)11yescharacteristic, complemented
181C22×C3D3×H(3,𝔽3)11yescharacteristic
182C2×D3—31no—
183C2×D3—31no—
184A4—33no—
185A4—63no—
186A4—91no—
187A4—181no—
188C32—21no—
189C32—31no—
190C32—61no—
191C32—123no—
192C32—121no—
193C32—123no—
194C32—121no—
195C32—243no—
196C32—243no—
197C32—243no—
198C32—246no—
199C32—241no—
200C32—241no—
201C32—361no—
202C32—721no—
203C32C2×C22⋊H(3,𝔽3)11yescharacteristic
204C32C3×D3×A411yescharacteristic
205C9—31no—
206C9—61no—
207C9—121no—
208C9—241no—
209C23—31noSylow
210C2×C3—31no—
211C2×C3—31no—
212C2×C3—31no—
213C2×C3—61no—
214C2×C3—91no—
215C2×C3—91no—
216C2×C3—91no—
217C2×C3—181no—
218C2×C3—271no—
219C2×C3—363no—
220C2×C3—1081no—
221D3—31no—
222D3#6636611yescharacteristic, direct product factor
223C22—91no—
224C22—91no—
225C22D3×AΣL(1,𝔽27)11yescharacteristic, complemented
226C3—21no—
227C3—31no—
228C3—61no—
229C3—123no—
230C3—243no—
231C3—361no—
232C3—721no—
233C3C2×#6636611yescharacteristic, complemented
234C3D3×C22⋊H(3,𝔽3)11yescharacteristic
235C2—31no—
236C2—31no—
237C2—91no—
subgroupG/H
centerC3D3×C22⋊H(3,𝔽3)
commutator, cosocleC22×C33C2×C32
FrattiniC32C3×D3×A4
FittingC22×C3×3−1+2C2×C3
socleC22×C32C2×H(3,𝔽3)
hypercenter3−1+2D3×A4
hypocenterC22×C3C2×AΣL(1,𝔽27)
LCSG ▷ C22×C33 ▷ C22×C32 ▷ C22×C3
UCSC1 ◁ C3 ◁ C32 ◁ 3−1+2

Complements

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

NH ≅ G/Ntype
1. C3×#66366C2semidirect
2. C32×D3×A4C3semidirect
3. C22×D3×3−1+2C3semidirect
4. D3×C22⋊H(3,𝔽3)C3semidirect
5. D3×#1094C3semidirect
8. C33×A4C2×C3semidirect
9. C22×C3×3−1+2C2×C3semidirect
12. C3×C22⋊H(3,𝔽3)C2×C3semidirect
13. C3×#1094C2×C3semidirect
18. #66366D3direct (N × H)
34. D3×3−1+2A4semidirect
46. C32×A4C3×D3semidirect
51. C22×3−1+2C3×D3semidirect
57. C22⋊H(3,𝔽3)C3×D3semidirect
60. #1094C3×D3semidirect
64. C3×3−1+2C2×A4semidirect
141. 3−1+2D3×A4semidirect
149. C22×D3AΣL(1,𝔽27)semidirect
180. C22×C3C2×AΣL(1,𝔽27)semidirect
222. D3#66366direct (N × H)
225. C22D3×AΣL(1,𝔽27)semidirect
233. C3C2×#66366semidirect

Maximal subgroups

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

subgroupindex
C3×#663662
C32×D3×A43
C22×D3×3−1+23
D3×C22⋊H(3,𝔽3)3
D3×#10943
C2×#663663
D3×AΣL(1,𝔽27)4