Finite Group Databasebeta

← C3×#10620045 #14519196

Subgroups — C3×#10620045 #14519196

Order 1944.

442 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 58 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
2C3×C9⋊S4C311yesmaximal, characteristic, complemented
3#10620045C313yesmaximal, direct product factor
4C3×(C3⋊S4)⋊C3—31nomaximal
5C3×((C22⋊C9)⋊C2)⋊C3—32nomaximal
6C32×#611—31nomaximal
7C3×#4207—41nomaximal
8C22×C32×C9D311yescharacteristic, complemented
9C2×C32×D9—31no—
10C3×C22⋊H(3,𝔽3)D311yescharacteristic
11C3×#1094D312yescomplemented
12#66436—23no—
13#66436—23no—
14#66436—26no—
15#66436C2×C313yescomplemented
16C3×C9⋊A4—21no—
17C3×C9⋊A4—22no—
18C3×C9×A4—21no—
19C3×C9×A4C2×C311yescharacteristic, complemented
20C32×Dic9—31no—
21C3×#737—41noSylow
22C3×C3⋊S4—31no—
23C32×#67—91no—
24C9⋊S4C3211yescharacteristic, complemented
25(C3⋊S4)⋊C3—33no—
26C3×(C22⋊C9)⋊C2—32no—
27((C22⋊C9)⋊C2)⋊C3—36no—
28C3×#611—31no—
29C3×#611—33no—
30C2×C32×C9—31no—
31#4207—43no—
32C3×C3⋊D9—41no—
33C3×AGL(1,ℤ/9)—122no—
34C3×(C3⋊D3)⋊C3—121no—
35C32×D9—61no—
36C22×C33C3⋊D311yescharacteristic
37C2×C32×D3—91no—
38C32×A4—21no—
39C32×A4C3×D311yescharacteristic
40C32×Dic3—91no—
41C22×C3×C9—21no—
42C22×C3×C9—23no—
43C22×C3×C9C3×D311yescharacteristic
44C22×C3×C9C3×D313yescomplemented
45C2×C3×D9—31no—
46C2×C3×D9—33no—
47C22⋊H(3,𝔽3)—23no—
48C22⋊H(3,𝔽3)C3×D313yes—
49#1094—26no—
50#1094C3×D316yescomplemented
51C3×C22⋊C9—22no—
52C3×C22⋊C9C3×D312yes—
53C9⋊A4—26no—
54C9⋊A4—212no—
55C9⋊A4—23no—
56C9⋊A4—26no—
57C9×A4—26no—
58C9×A4—21no—
59C9×A4—23no—
60C9×A4—21no—
61C9×A4—22no—
62C9×A4C2×C3211yescharacteristic, complemented
63C3×Dic9—31no—
64C3×Dic9—33no—
65#737—43no—
66#737—83no—
67#737—86no—
68#737—83no—
69C3×3−1+2—42no—
70C3×3−1+2—82no—
71C3×3−1+2—81no—
72C3×H(3,𝔽3)—41no—
73C32×C9—41no—
74C32×C9—81no—
75C32×C9S411yescharacteristic, complemented
76C3⋊S4—31no—
77C3×S4—271no—
78C32×D4—271no—
79C3×#67—93no—
80C3×#67—91no—
81(C22⋊C9)⋊C2—32no—
82#611—31no—
83C2×C33—31no—
84C3×C3⋊D3—121no—
85C32×D3—181no—
86C2×C3×C9—31no—
87C2×C3×C9—33no—
88C2×C3×C9—61no—
89C2×C3×C9—63no—
90C3⋊D9—41no—
91AGL(1,ℤ/9)—126no—
92(C3⋊D3)⋊C3—123no—
93C3×D9—61no—
94C3×D9—63no—
95C3×D9—122no—
96C22×C32—31no—
97C22×C32—61no—
98C22×C32—271no—
99C22×C32C3×C3⋊D311yescharacteristic
100C22×C32C3×C3⋊D313yes—
101C2×C3×D3—91no—
102C2×C3×D3—93no—
103C3×A4—21no—
104C3×A4—23no—
105C3×A4—31no—
106C3×A4—61no—
107C3×A4—62no—
108C3×A4—61no—
109C3×A4C32×D311yescharacteristic
110C32×C4—271no—
111C3×Dic3—93no—
112C3×Dic3—91no—
113C22×C9—21no—
114C22×C9—23no—
115C22×C9C32×D311yescharacteristic
116C2×D9—31no—
117C22⋊C9—26no—
118C22⋊C9—22no—
119C22⋊C9C32×D312yes—
120Dic9—31no—
121C33—41no—
122C33—81no—
123C33C3⋊S411yescharacteristic
1243−1+2—46no—
1253−1+2—86no—
1263−1+2—83no—
1273−1+2—812no—
1283−1+2—86no—
1293−1+2—86no—
130H(3,𝔽3)—43no—
131H(3,𝔽3)—83no—
132C3×C9—21no—
133C3×C9—23no—
134C3×C9—41no—
135C3×C9—42no—
136C3×C9—82no—
137C3×C9—81no—
138C3×C9—86no—
139C3×C9—82no—
140C3×C9—81no—
141C3×C9—83no—
142C3×C9C3×S411yescharacteristic
143C3×C9C3×S413yescomplemented
144S4—271no—
145C3×D4—273no—
146C3×D4—271no—
147#67—91no—
148C2×C32—31no—
149C2×C32—33no—
150C2×C32—31no—
151C2×C32—61no—
152C2×C32—63no—
153C2×C32—541no—
154C3⋊D3—121no—
155C3×D3—181no—
156C3×D3—183no—
157C3×D3—1081no—
158C2×C9—31no—
159C2×C9—61no—
160C2×C9—63no—
161D9—61no—
162D9—122no—
163C22×C3—21no—
164C22×C3—33no—
165C22×C3—273no—
166C22×C3—271no—
167C22×C3#420711yescharacteristic, complemented
168C22×C3C32×C3⋊D311yescharacteristic
169C2×D3—91no—
170A4—31no—
171A4—61no—
172A4—63no—
173C3×C4—273no—
174C3×C4—271no—
175Dic3—91no—
176C32—31no—
177C32—41no—
178C32—61no—
179C32—83no—
180C32—81no—
181C32—121no—
182C32—241no—
183C32—242no—
184C32—241no—
185C32C3×C3⋊S411yescharacteristic
186C32C3×C3⋊S413yes—
187C9—21no—
188C9—23no—
189C9—42no—
190C9—82no—
191C9—86no—
192C9C32×S411yescharacteristic
193D4—271noSylow
194C2×C3—33no—
195C2×C3—31no—
196C2×C3—31no—
197C2×C3—61no—
198C2×C3—63no—
199C2×C3—543no—
200C2×C3—541no—
201D3—181no—
202D3—1081no—
203C22—271no—
204C22C3×#420711yescharacteristic, complemented
205C4—271no—
206C3—21no—
207C3—33no—
208C3—121no—
209C3—241no—
210C3—243no—
211C3#1062004511yescharacteristic, direct product factor
212C3C32×C3⋊S411yescharacteristic
213C2—31no—
214C2—541no—
subgroupG/H
center, hypercenterC3#10620045
commutator, cosocle, hypocenterC9×A4C2×C32
FrattiniC3C32×C3⋊S4
FittingC22×C32×C9D3
socleC22×C32C3×C3⋊D3
LCSG ▷ C9×A4
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×#66436C2semidirect
2. C3×C9⋊S4C3semidirect
3. #10620045C3direct (N × H)
8. C22×C32×C9D3semidirect
11. C3×#1094D3semidirect
15. #66436C2×C3semidirect
19. C3×C9×A4C2×C3semidirect
24. C9⋊S4C32semidirect
44. C22×C3×C9C3×D3semidirect
50. #1094C3×D3semidirect
62. C9×A4C2×C32semidirect
75. C32×C9S4semidirect
143. C3×C9C3×S4semidirect
167. C22×C3#4207semidirect
204. C22C3×#4207semidirect
211. C3#10620045direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#664362
C3×C9⋊S43
#106200453
C3×(C3⋊S4)⋊C33
C3×((C22⋊C9)⋊C2)⋊C33
C32×#6113
C3×#42074