Finite Group Databasebeta

← D3×A4×3−1+2 #14519241

Subgroups — D3×A4×3−1+2 #14519241

Order 1944.

591 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 591 conjugacy classes of subgroups — too many to draw. Only its 117 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×A4×3−1+2C211yesmaximal, characteristic, complemented
2C32×D3×A4C311yesmaximal, characteristic
3C22×D3×3−1+2C311yesmaximal, characteristic, complemented
4C2×A4×3−1+2—31nomaximal
5D3×#1094C312yesmaximal, complemented
6D3×C9⋊A4C316yesmaximal, complemented
7D3×C9×A4C313yesmaximal, complemented
8C3×D3×3−1+2—41nomaximal
9C33×A4C2×C311yescharacteristic
10C22×C3×3−1+2C2×C311yescharacteristic, complemented
11C2×D3×3−1+2—31no—
12C2×D3×3−1+2—31no—
13C3×#1094C2×C312yescomplemented
14A4×3−1+2—21no—
15A4×3−1+2—21no—
16A4×3−1+2—22no—
17A4×3−1+2—26no—
18A4×3−1+2—23no—
19A4×3−1+2D311yescharacteristic, direct product factor
20C3×C9⋊A4C2×C316yescomplemented
21C3×C9×A4C2×C313yescomplemented
22C32×3−1+2—41noSylow
23C22×C32×D3C3211yescharacteristic
24C2×C32×A4—31no—
25C3×D3×A4—33no—
26C3×D3×A4C3212yes—
27C3×D3×A4C3211yescharacteristic
28C23×3−1+2—31no—
29C22×D3×C9C3213yescomplemented
30C2×#1094—32no—
31C2×C9⋊A4—36no—
32C2×C9×A4—33no—
33D3×C22⋊C9C3216yescomplemented
34C33×D3—41no—
35C2×C3×3−1+2—31no—
36C2×C3×3−1+2—121no—
37D3×3−1+2—31no—
38D3×3−1+2—42no—
39D3×3−1+2—46no—
40D3×3−1+2A411yescharacteristic, direct product factor
41C3×D3×C9—43no—
42C22×C33C2×C3211yescharacteristic
43C2×C32×D3—31no—
44C2×C32×D3—31no—
45C32×A4—21no—
46C32×A4—22no—
47C32×A4—21no—
48C32×A4—33no—
49C32×A4—63no—
50C32×A4C3×D311yescharacteristic
51C32×A4C2×C3211yescharacteristic
52C32×A4C2×C3212yes—
53C22×3−1+2—21no—
54C22×3−1+2—23no—
55C22×3−1+2—91no—
56C22×3−1+2—91no—
57C22×3−1+2C3×D311yescharacteristic, complemented
58C22×C3×C9C2×C3213yescomplemented
59C2×D3×C9—33no—
60C2×D3×C9—33no—
61#1094—22no—
62#1094—26no—
63#1094C3×D312yescomplemented
64C3×C22⋊C9C2×C3216yescomplemented
65C9⋊A4—26no—
66C9⋊A4—26no—
67C9⋊A4—212no—
68C9⋊A4C3×D316yescomplemented
69C9×A4—23no—
70C9×A4—23no—
71C9×A4—26no—
72C9×A4C3×D313yescomplemented
73C34—41no—
74C3×3−1+2—41no—
75C3×3−1+2—42no—
76C3×3−1+2—46no—
77C3×3−1+2—83no—
78C3×3−1+2—82no—
79C3×3−1+2—86no—
80C3×3−1+2—81no—
81C3×3−1+2—81no—
82C3×3−1+2C2×A411yescharacteristic, complemented
83C32×C9—43no—
84C23×C32—31no—
85C22×C3×D3—31no—
86C22×C3×D3C3311yescharacteristic
87C2×C3×A4—31no—
88C2×C3×A4—32no—
89C2×C3×A4—93no—
90D3×A4—32no—
91D3×A43−1+213yesdirect product factor
92C23×C9—33no—
93C2×C22⋊C9—36no—
94C2×C33—31no—
95C2×C33—121no—
96C32×D3—31no—
97C32×D3—41no—
98C32×D3—42no—
99C32×D3—123no—
100C32×D3C3×A411yescharacteristic
101C2×3−1+2—31no—
102C2×3−1+2—31no—
103C2×3−1+2—63no—
104C2×3−1+2—61no—
105C2×3−1+2—91no—
106C2×3−1+2—126no—
107C2×3−1+2—122no—
108C2×C3×C9—33no—
109C2×C3×C9—123no—
110D3×C9—33no—
111D3×C9—46no—
112D3×C9C3×A413yescomplemented
113C22×C32—21no—
114C22×C32—31no—
115C22×C32—61no—
116C22×C32—91no—
117C22×C32—91no—
118C22×C32C32×D311yescharacteristic
119C22×C32C2×C3311yescharacteristic
120C2×C3×D3—31no—
121C2×C3×D3—31no—
122C2×C3×D3—91no—
123C2×C3×D3—91no—
124C3×A4—21no—
125C3×A4—23no—
126C3×A4—22no—
127C3×A4—33no—
128C3×A4—32no—
129C3×A4—66no—
130C3×A4—63no—
131C3×A4—62no—
132C3×A4—63no—
133C3×A4C2×3−1+213yescomplemented
134C3×A4C32×D312yes—
135C3×A4C32×D311yescharacteristic
136C22×C9—23no—
137C22×C9—93no—
138C22×C9—93no—
139C22×C9C32×D313yescomplemented
140C22⋊C9—26no—
141C22⋊C9C32×D316yescomplemented
142C33—41no—
143C33—41no—
144C33—42no—
145C33—81no—
146C33—82no—
147C33—81no—
148C33—123no—
149C33—243no—
150C33C2×C3×A411yescharacteristic
1513−1+2—21no—
1523−1+2—23no—
1533−1+2—42no—
1543−1+2—46no—
1553−1+2—812no—
1563−1+2—86no—
1573−1+2—86no—
1583−1+2—82no—
1593−1+2—86no—
1603−1+2D3×A411yescharacteristic, direct product factor
161C3×C9—43no—
162C3×C9—46no—
163C3×C9—86no—
164C3×C9—83no—
165C3×C9—83no—
166C3×C9C2×C3×A413yescomplemented
167C23×C3—31no—
168C23×C3—91no—
169C22×D3C3×3−1+211yescharacteristic, complemented
170C2×A4—33no—
171C2×A4—92no—
172C2×C32—31no—
173C2×C32—31no—
174C2×C32—31no—
175C2×C32—61no—
176C2×C32—91no—
177C2×C32—91no—
178C2×C32—121no—
179C2×C32—122no—
180C2×C32—181no—
181C2×C32—363no—
182C3×D3—31no—
183C3×D3—31no—
184C3×D3—43no—
185C3×D3—91no—
186C3×D3—122no—
187C3×D3C32×A411yescharacteristic
188C2×C9—33no—
189C2×C9—33no—
190C2×C9—63no—
191C2×C9—93no—
192C2×C9—126no—
193C22×C3—21no—
194C22×C3—31no—
195C22×C3—61no—
196C22×C3—91no—
197C22×C3—91no—
198C22×C3—271no—
199C22×C3—271no—
200C22×C3C2×C3×3−1+211yescharacteristic, complemented
201C22×C3C33×D311yescharacteristic
202C2×D3—31no—
203C2×D3—31no—
204A4—23no—
205A4—32no—
206A4—62no—
207A4D3×3−1+213yesdirect product factor
208C32—21no—
209C32—31no—
210C32—41no—
211C32—43no—
212C32—42no—
213C32—61no—
214C32—83no—
215C32—81no—
216C32—82no—
217C32—123no—
218C32—122no—
219C32—242no—
220C32—243no—
221C32—243no—
222C32—246no—
223C32C3×D3×A411yescharacteristic
224C32C2×C32×A411yescharacteristic
225C9—23no—
226C9—46no—
227C9—86no—
228C9C3×D3×A413yescomplemented
229C23—31noSylow
230C2×C3—31no—
231C2×C3—31no—
232C2×C3—31no—
233C2×C3—61no—
234C2×C3—91no—
235C2×C3—91no—
236C2×C3—91no—
237C2×C3—123no—
238C2×C3—181no—
239C2×C3—271no—
240C2×C3—362no—
241D3—31no—
242D3A4×3−1+211yescharacteristic, direct product factor
243C22—91no—
244C22—91no—
245C22C3×D3×3−1+211yescharacteristic, complemented
246C3—21no—
247C3—31no—
248C3—43no—
249C3—61no—
250C3—83no—
251C3—122no—
252C3—242no—
253C3C2×A4×3−1+211yescharacteristic, complemented
254C3C32×D3×A411yescharacteristic
255C2—31no—
256C2—31no—
257C2—91no—
subgroupG/H
center, FrattiniC3C32×D3×A4
commutator, socle, cosocleC22×C32C2×C33
FittingC22×C3×3−1+2C2×C3
prime radicalC32×D3×A4C3
hypercenter3−1+2D3×A4
hypocenterC22×C3C2×C3×3−1+2
LCSG ▷ C22×C32 ▷ C22×C3
UCSC1 ◁ C3 ◁ 3−1+2

Complements

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

NH ≅ G/Ntype
1. C3×A4×3−1+2C2semidirect
3. C22×D3×3−1+2C3semidirect
5. D3×#1094C3semidirect
6. D3×C9⋊A4C3semidirect
7. D3×C9×A4C3semidirect
10. C22×C3×3−1+2C2×C3semidirect
13. C3×#1094C2×C3semidirect
19. A4×3−1+2D3direct (N × H)
20. C3×C9⋊A4C2×C3semidirect
21. C3×C9×A4C2×C3semidirect
29. C22×D3×C9C32semidirect
33. D3×C22⋊C9C32semidirect
40. D3×3−1+2A4direct (N × H)
57. C22×3−1+2C3×D3semidirect
58. C22×C3×C9C2×C32semidirect
63. #1094C3×D3semidirect
64. C3×C22⋊C9C2×C32semidirect
68. C9⋊A4C3×D3semidirect
72. C9×A4C3×D3semidirect
82. C3×3−1+2C2×A4semidirect
91. D3×A43−1+2direct (N × H)
112. D3×C9C3×A4semidirect
133. C3×A4C2×3−1+2semidirect
139. C22×C9C32×D3semidirect
141. C22⋊C9C32×D3semidirect
160. 3−1+2D3×A4direct (N × H)
166. C3×C9C2×C3×A4semidirect
169. C22×D3C3×3−1+2semidirect
200. C22×C3C2×C3×3−1+2semidirect
207. A4D3×3−1+2direct (N × H)
228. C9C3×D3×A4semidirect
242. D3A4×3−1+2direct (N × H)
245. C22C3×D3×3−1+2semidirect
253. C3C2×A4×3−1+2semidirect

Maximal subgroups

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

subgroupindex
C3×A4×3−1+22
C32×D3×A43
C22×D3×3−1+23
C2×A4×3−1+23
D3×#10943
D3×C9⋊A43
D3×C9×A43
C3×D3×3−1+24