Finite Group Databasebeta

← C3×#10620047 #14519197

Subgroups — C3×#10620047 #14519197

Order 1944.

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

normal subgroups only

This group has 450 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×#66437C211yesmaximal, characteristic, complemented
2C3×C3⋊((C22⋊C9)⋊C2)C311yesmaximal, characteristic, complemented
3#10620047C313yesmaximal, direct product factor
4C32×(C22⋊C9)⋊C2—31nomaximal
5C3×((C22⋊C9)⋊C2)⋊C3—32nomaximal
6C3×#638⋊C3—31nomaximal
7C3×#4207—41nomaximal
8C22×C3×H(3,𝔽3)D311yescharacteristic
9C2×C3×(C3⋊D3)⋊C3—31no—
10C3×#1094—21no—
11C3×#1094—22no—
12C3×#1094D312yescomplemented
13C32×C22⋊C9—21no—
14C32×C22⋊C9D311yescharacteristic, complemented
15C32×C22⋊C9C2×C311yescharacteristic, complemented
16#66437—23no—
17#66437—26no—
18#66437—23no—
19#66437C2×C313yescomplemented
20C3×(C3⋊Dic3)⋊C3—31no—
21C3×#737—41noSylow
22C3×#638—31no—
23C32×#67—91no—
24C3⋊((C22⋊C9)⋊C2)C3211yescharacteristic, complemented
25C3×(C22⋊C9)⋊C2—32no—
26C3×(C22⋊C9)⋊C2—31no—
27C3×(C22⋊C9)⋊C2—33no—
28((C22⋊C9)⋊C2)⋊C3—36no—
29#638⋊C3—33no—
30C2×C3×H(3,𝔽3)—31no—
31#4207—43no—
32C3×C3⋊D9—41no—
33C3×AGL(1,ℤ/9)—122no—
34C3×(C3⋊D3)⋊C3—61no—
35C32×D9—121no—
36C22×C33—21no—
37C22×C33C3×D311yescharacteristic
38C22×C33C3⋊D311yescharacteristic
39C2×C3×C3⋊D3—31no—
40C2×C32×D3—91no—
41C3×C3⋊Dic3—31no—
42C32×Dic3—91no—
43C22×H(3,𝔽3)—23no—
44C22×H(3,𝔽3)C3×D313yes—
45C2×(C3⋊D3)⋊C3—33no—
46#1094—26no—
47#1094—212no—
48#1094—23no—
49#1094—26no—
50#1094—26no—
51#1094C3×D316yescomplemented
52C3×C22⋊C9—26no—
53C3×C22⋊C9—21no—
54C3×C22⋊C9—23no—
55C3×C22⋊C9—22no—
56C3×C22⋊C9—21no—
57C3×C22⋊C9—22no—
58C3×C22⋊C9—21no—
59C3×C22⋊C9—23no—
60C3×C22⋊C9C3×D311yescharacteristic
61C3×C22⋊C9C3×D312yes—
62C3×C22⋊C9C3×D313yescomplemented
63C3×C22⋊C9C2×C3211yescharacteristic, complemented
64(C3⋊Dic3)⋊C3—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)S411yescharacteristic
73C32×C9—41no—
74C32×C9—41no—
75C32×C9—81no—
76C32×D4—271no—
77#638—31no—
78C3×#67—93no—
79C3×#67—91no—
80C3×#67—271no—
81(C22⋊C9)⋊C2—32no—
82(C22⋊C9)⋊C2—31no—
83C2×C33—31no—
84C2×C33—31no—
85C2×C33—61no—
86C3×C3⋊D3—61no—
87C32×D3—181no—
88C2×H(3,𝔽3)—33no—
89C2×H(3,𝔽3)—63no—
90C3⋊D9—41no—
91AGL(1,ℤ/9)—126no—
92(C3⋊D3)⋊C3—63no—
93C3×D9—121no—
94C3×D9—123no—
95C3×D9—122no—
96C22×C32—21no—
97C22×C32—23no—
98C22×C32—31no—
99C22×C32—31no—
100C22×C32—61no—
101C22×C32—61no—
102C22×C32—62no—
103C22×C32—61no—
104C22×C32—271no—
105C22×C32C32×D311yescharacteristic
106C22×C32C3×C3⋊D311yescharacteristic
107C22×C32C3×C3⋊D313yes—
108C2×C3⋊D3—31no—
109C2×C3×D3—93no—
110C2×C3×D3—91no—
111C2×C3×D3—271no—
112C32×C4—271no—
113C3⋊Dic3—31no—
114C3×Dic3—93no—
115C3×Dic3—91no—
116C3×Dic3—271no—
117C22⋊C9—21no—
118C22⋊C9—26no—
119C22⋊C9—22no—
120C22⋊C9—23no—
121C22⋊C9C32×D311yescharacteristic
122C22⋊C9C32×D312yes—
123C33—21no—
124C33C3×S411yescharacteristic
125C33C3⋊S411yescharacteristic
1263−1+2—46no—
1273−1+2—86no—
1283−1+2—812no—
1293−1+2—86no—
1303−1+2—83no—
1313−1+2—86no—
132H(3,𝔽3)—23no—
133H(3,𝔽3)C3×S413yes—
134C3×C9—41no—
135C3×C9—41no—
136C3×C9—42no—
137C3×C9—43no—
138C3×C9—81no—
139C3×C9—82no—
140C3×C9—83no—
141C3×C9—86no—
142C3×C9—81no—
143C3×C9—81no—
144C3×C9—83no—
145C3×C9—82no—
146C3×D4—273no—
147C3×D4—271no—
148#67—91no—
149#67—271no—
150C2×C32—31no—
151C2×C32—31no—
152C2×C32—33no—
153C2×C32—63no—
154C2×C32—61no—
155C2×C32—91no—
156C2×C32—91no—
157C2×C32—181no—
158C2×C32—181no—
159C2×C32—181no—
160C2×C32—182no—
161C2×C32—541no—
162C3⋊D3—61no—
163C3×D3—181no—
164C3×D3—183no—
165C3×D3—541no—
166D9—121no—
167D9—122no—
168C22×C3—21no—
169C22×C3—31no—
170C22×C3—33no—
171C22×C3—61no—
172C22×C3—63no—
173C22×C3—271no—
174C22×C3—273no—
175C22×C3#420711yescharacteristic, complemented
176C22×C3C32×C3⋊D311yescharacteristic
177C2×D3—91no—
178C2×D3—271no—
179C3×C4—271no—
180C3×C4—273no—
181Dic3—91no—
182Dic3—271no—
183C32—21no—
184C32—23no—
185C32—31no—
186C32—31no—
187C32—61no—
188C32—61no—
189C32—62no—
190C32—61no—
191C32C32×S411yescharacteristic
192C32C3×C3⋊S411yescharacteristic
193C32C3×C3⋊S413yes—
194C9—41no—
195C9—42no—
196C9—81no—
197C9—82no—
198C9—83no—
199C9—86no—
200D4—271noSylow
201C2×C3—31no—
202C2×C3—31no—
203C2×C3—61no—
204C2×C3—91no—
205C2×C3—93no—
206C2×C3—181no—
207C2×C3—183no—
208C2×C3—543no—
209C2×C3—541no—
210D3—181no—
211D3—541no—
212C22—271no—
213C22C3×#420711yescharacteristic, complemented
214C4—271no—
215C3—21no—
216C3—31no—
217C3—33no—
218C3—61no—
219C3—63no—
220C3#1062004711yescharacteristic, direct product factor
221C3C32×C3⋊S411yescharacteristic
222C2—31no—
223C2—541no—
subgroupG/H
center, hypercenterC3#10620047
commutator, cosocle, hypocenterC3×C22⋊C9C2×C32
FrattiniC3C32×C3⋊S4
FittingC22×C3×H(3,𝔽3)D3
socleC22×C32C3×C3⋊D3
LCSG ▷ C3×C22⋊C9
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×#66437C2semidirect
2. C3×C3⋊((C22⋊C9)⋊C2)C3semidirect
3. #10620047C3direct (N × H)
12. C3×#1094D3semidirect
14. C32×C22⋊C9D3semidirect
15. C32×C22⋊C9C2×C3semidirect
19. #66437C2×C3semidirect
24. C3⋊((C22⋊C9)⋊C2)C32semidirect
51. #1094C3×D3semidirect
62. C3×C22⋊C9C3×D3semidirect
63. C3×C22⋊C9C2×C32semidirect
175. C22×C3#4207semidirect
213. C22C3×#4207semidirect
220. C3#10620047direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#664372
C3×C3⋊((C22⋊C9)⋊C2)3
#106200473
C32×(C22⋊C9)⋊C23
C3×((C22⋊C9)⋊C2)⋊C33
C3×#638⋊C33
C3×#42074