Finite Group Databasebeta

← C3×#10620070 #14519249

Subgroups — C3×#10620070 #14519249

Order 1944.

467 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 467 conjugacy classes of subgroups — too many to draw. Only its 60 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×#66436C211yesmaximal, characteristic, complemented
2C22×C3×C3⋊D9C311yesmaximal, characteristic, complemented
3#10620070C313yesmaximal, direct product factor
4C3×(C3⋊D3)⋊A4—31nomaximal
5C3×A4×D9—31nomaximal
6C3×D9⋊A4—32nomaximal
7C3×#4207—41nomaximal
8C22×C32×C9C2×C311yescharacteristic, complemented
9C2×C3×C3⋊D9—31no—
10C2×C3×C3⋊D9—31no—
11C3×C22⋊H(3,𝔽3)D311yescharacteristic
12C3×#1094—21no—
13#66436—23no—
14#66436—26no—
15#66436—23no—
16#66436C2×C313yescomplemented
17C3×C9⋊A4—22no—
18C3×C9⋊A4D312yescomplemented
19C3×C9×A4—21no—
20C3×C9×A4D311yescharacteristic, complemented
21C3×#737—41noSylow
22C22×C3×C3⋊D3—31no—
23C3×D3×A4—91no—
24C22×C3⋊D9C3211yescharacteristic, complemented
25C22×C3×D9—32no—
26C22×C3×D9—31no—
27(C3⋊D3)⋊A4—33no—
28A4×D9—33no—
29D9⋊A4—36no—
30C2×C32×C9—31no—
31#4207—43no—
32C3×C3⋊D9—31no—
33C3×C3⋊D9A411yescharacteristic, complemented
34C3×AGL(1,ℤ/9)—122no—
35C3×(C3⋊D3)⋊C3—121no—
36C32×D9—121no—
37C22×C33C3×D311yescharacteristic
38C2×C3×C3⋊D3—91no—
39C2×C3×C3⋊D3—91no—
40C32×A4—21no—
41C32×A4C3⋊D311yescharacteristic
42C22×C3×C9—21no—
43C22×C3×C9—22no—
44C22×C3×C9—21no—
45C22×C3×C9C3×D311yescharacteristic
46C22×C3×C9C3×D312yes—
47C22×C3×C9C2×C3211yescharacteristic, complemented
48C2×C3⋊D9—31no—
49C2×C3⋊D9—31no—
50C2×C3×D9—91no—
51C2×C3×D9—92no—
52C2×C3×D9—92no—
53C2×C3×D9—91no—
54C22⋊H(3,𝔽3)—23no—
55C22⋊H(3,𝔽3)C3×D313yes—
56#1094—26no—
57#1094—23no—
58C3×C22⋊C9—22no—
59C3×C22⋊C9—21no—
60C9⋊A4—212no—
61C9⋊A4—26no—
62C9⋊A4—26no—
63C9⋊A4C3×D316yescomplemented
64C9×A4—26no—
65C9×A4—23no—
66C9×A4—23no—
67C9×A4C3×D313yescomplemented
68#737—43no—
69#737—83no—
70#737—83no—
71#737—86no—
72C3×3−1+2—42no—
73C3×3−1+2—81no—
74C3×3−1+2—82no—
75C3×H(3,𝔽3)—41no—
76C32×C9—41no—
77C32×C9—81no—
78C32×C9C2×A411yescharacteristic, complemented
79C22×C3⋊D3—31no—
80C22×C3×D3—91no—
81C22×C3×D3—271no—
82C2×C3×A4—271no—
83D3×A4—93no—
84C22×D9—32no—
85C22×D9—31no—
86C2×C33—31no—
87C3×C3⋊D3—31no—
88C3×C3⋊D3—91no—
89C32×D3—361no—
90C2×C3×C9—31no—
91C2×C3×C9—31no—
92C2×C3×C9—32no—
93C2×C3×C9—61no—
94C2×C3×C9—62no—
95C2×C3×C9—61no—
96C3⋊D9—31no—
97C3⋊D9C3×A411yescharacteristic, complemented
98AGL(1,ℤ/9)—126no—
99(C3⋊D3)⋊C3—123no—
100C3×D9—31no—
101C3×D9—32no—
102C3×D9—91no—
103C3×D9—92no—
104C3×D9—123no—
105C22×C32—21no—
106C22×C32—31no—
107C22×C32—61no—
108C22×C32C32×D311yescharacteristic
109C22×C32C3×C3⋊D311yescharacteristic
110C2×C3⋊D3—91no—
111C2×C3⋊D3—91no—
112C2×C3×D3—271no—
113C2×C3×D3—273no—
114C2×C3×D3—273no—
115C2×C3×D3—271no—
116C3×A4—23no—
117C3×A4—31no—
118C3×A4—61no—
119C3×A4—62no—
120C3×A4—61no—
121C3×A4C3×C3⋊D313yes—
122C22×C9—21no—
123C22×C9—22no—
124C22×C9C32×D311yescharacteristic
125C22×C9C32×D312yes—
126C2×D9—91no—
127C2×D9—92no—
128C2×D9—92no—
129C2×D9—91no—
130C22⋊C9—26no—
131C22⋊C9—23no—
132C33—41no—
133C33—81no—
134C33D3×A411yescharacteristic
1353−1+2—46no—
1363−1+2—86no—
1373−1+2—812no—
1383−1+2—86no—
1393−1+2—83no—
1403−1+2—86no—
141H(3,𝔽3)—43no—
142H(3,𝔽3)—83no—
143C3×C9—21no—
144C3×C9—22no—
145C3×C9—21no—
146C3×C9—43no—
147C3×C9—83no—
148C3×C9—86no—
149C3×C9—81no—
150C3×C9—82no—
151C3×C9—83no—
152C3×C9D3×A411yescharacteristic
153C3×C9D3×A412yes—
154C3×C9C2×C3×A411yescharacteristic, complemented
155C23×C3—271no—
156C22×D3—91no—
157C22×D3—271no—
158C2×A4—273no—
159C2×C32—31no—
160C2×C32—33no—
161C2×C32—31no—
162C2×C32—61no—
163C2×C32—63no—
164C2×C32—1081no—
165C3⋊D3—31no—
166C3⋊D3—91no—
167C3×D3—91no—
168C3×D3—271no—
169C3×D3—273no—
170C3×D3—271no—
171C3×D3—363no—
172C2×C9—31no—
173C2×C9—32no—
174C2×C9—61no—
175C2×C9—62no—
176D9—31no—
177D9—32no—
178D9—91no—
179D9—92no—
180C22×C3—21no—
181C22×C3—31no—
182C22×C3—61no—
183C22×C3—811no—
184C22×C3—811no—
185C22×C3#420711yescharacteristic, complemented
186C22×C3C32×C3⋊D311yescharacteristic
187C2×D3—271no—
188C2×D3—273no—
189C2×D3—273no—
190C2×D3—271no—
191A4—33no—
192A4—63no—
193C32—21no—
194C32—31no—
195C32—43no—
196C32—61no—
197C32—83no—
198C32—121no—
199C32—241no—
200C32—242no—
201C32—241no—
202C32C3×D3×A411yescharacteristic
203C32A4×C3⋊D311yescharacteristic
204C9—21no—
205C9—22no—
206C9—83no—
207C9—86no—
208C9C3×D3×A411yescharacteristic
209C9C3×D3×A412yes—
210C23—271noSylow
211C2×C3—33no—
212C2×C3—31no—
213C2×C3—31no—
214C2×C3—61no—
215C2×C3—63no—
216C2×C3—271no—
217C2×C3—811no—
218C2×C3—1083no—
219D3—91no—
220D3—271no—
221D3—273no—
222D3—271no—
223C22—811no—
224C22—811no—
225C22C3×#420711yescharacteristic, complemented
226C3—21no—
227C3—31no—
228C3—61no—
229C3—123no—
230C3—243no—
231C3#1062007011yescharacteristic, direct product factor
232C3C3×A4×C3⋊D311yescharacteristic
233C2—31no—
234C2—271no—
235C2—811no—
subgroupG/H
center, hypercenterC3#10620070
commutator, cosocle, hypocenterC22×C3×C9C2×C32
FrattiniC3C3×A4×C3⋊D3
FittingC22×C32×C9C2×C3
socleC22×C32C3×C3⋊D3
LCSG ▷ C22×C3×C9
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×#66436C2semidirect
2. C22×C3×C3⋊D9C3semidirect
3. #10620070C3direct (N × H)
8. C22×C32×C9C2×C3semidirect
16. #66436C2×C3semidirect
18. C3×C9⋊A4D3semidirect
20. C3×C9×A4D3semidirect
24. C22×C3⋊D9C32semidirect
33. C3×C3⋊D9A4semidirect
47. C22×C3×C9C2×C32semidirect
63. C9⋊A4C3×D3semidirect
67. C9×A4C3×D3semidirect
78. C32×C9C2×A4semidirect
97. C3⋊D9C3×A4semidirect
154. C3×C9C2×C3×A4semidirect
185. C22×C3#4207semidirect
225. C22C3×#4207semidirect
231. C3#10620070direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#664362
C22×C3×C3⋊D93
#106200703
C3×(C3⋊D3)⋊A43
C3×A4×D93
C3×D9⋊A43
C3×#42074