Finite Group Databasebeta

← C3×#10619770 #14518184

Subgroups — C3×#10619770 #14518184

Order 1944.

371 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 371 conjugacy classes of subgroups — too many to draw. Only its 48 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×(C3×A4)⋊C9C211yesmaximal, characteristic, complemented
2C3×A4×C3⋊D3—31nomaximal
3C22×C3×C3⋊D9C311yesmaximal, characteristic, complemented
4#10619770C313yesmaximal, direct product factor
5C3×#4169—41nomaximal
6C33×A4D311yescharacteristic
7C22×C32×C9C2×C311yescharacteristic, complemented
8C2×C3×C3⋊D9—31no—
9C2×C3×C3⋊D9—31no—
10C32×C22⋊C9—21no—
11(C3×A4)⋊C9—23no—
12(C3×A4)⋊C9C2×C313yescomplemented
13C3×C32⋊C9—41noSylow
14C22×C3×C3⋊D3—31no—
15A4×C3⋊D3—33no—
16C3×D3×A4—91no—
17C3×D3×A4—92no—
18C3×D3×A4—91no—
19C22×C3⋊D9C3211yescharacteristic, complemented
20C22×C3×D9—91no—
21C32×C3⋊D3—121no—
22C2×C32×C9—31no—
23C3×C3⋊D9—31no—
24C3×C3⋊D9A411yescharacteristic, complemented
25#4169—43no—
26C22×C33C3×D311yescharacteristic
27C2×C3×C3⋊D3—91no—
28C2×C3×C3⋊D3—91no—
29C32×A4—21no—
30C32×A4—23no—
31C32×A4—31no—
32C32×A4—32no—
33C32×A4—61no—
34C32×A4—62no—
35C32×A4D911yescharacteristic, complemented
36C32×A4C3×D313yes—
37C22×C3×C9—21no—
38C22×C3×C9—31no—
39C22×C3×C9—61no—
40C22×C3×C9C2×C3211yescharacteristic, complemented
41C2×C3⋊D9—31no—
42C2×C3⋊D9—31no—
43C2×C3×D9—93no—
44C2×C3×D9—93no—
45C3×C22⋊C9—23no—
46C3×C22⋊C9—62no—
47C3×C22⋊C9—61no—
48C34—41no—
49C32×C9—81no—
50C32×C9C2×A411yescharacteristic, complemented
51C32⋊C9—43no—
52C32⋊C9—83no—
53C22×C3⋊D3—31no—
54C22×C3×D3—91no—
55C22×C3×D3—91no—
56C22×C3×D3—92no—
57C2×C3×A4—271no—
58D3×A4—93no—
59D3×A4—96no—
60D3×A4—93no—
61C22×D9—91no—
62C2×C33—31no—
63C3×C3⋊D3—31no—
64C3×C3⋊D3—91no—
65C3×C3⋊D3—123no—
66C32×D3—361no—
67C32×D3—362no—
68C32×D3—361no—
69C2×C3×C9—31no—
70C2×C3×C9—33no—
71C2×C3×C9—63no—
72C2×C3×C9—61no—
73C3⋊D9—31no—
74C3⋊D9C3×A411yescharacteristic, complemented
75C3×D9—91no—
76C3×D9—93no—
77C22×C32—21no—
78C22×C32—21no—
79C22×C32—22no—
80C22×C32C3×D911yescharacteristic
81C22×C32(C3⋊D3)⋊C311yescharacteristic
82C22×C32AGL(1,ℤ/9)12yes—
83C22×C32C32×D311yescharacteristic
84C2×C3⋊D3—91no—
85C2×C3⋊D3—91no—
86C2×C3×D3—271no—
87C2×C3×D3—272no—
88C2×C3×D3—271no—
89C2×C3×D3—271no—
90C2×C3×D3—272no—
91C2×C3×D3—271no—
92C3×A4—23no—
93C3×A4—31no—
94C3×A4—33no—
95C3×A4—36no—
96C3×A4—61no—
97C3×A4—63no—
98C3×A4—66no—
99C3×A4—62no—
100C3×A4—61no—
101C3×A4C3×D913yescomplemented
102C22×C9—31no—
103C22×C9—61no—
104C2×D9—93no—
105C2×D9—93no—
106C22⋊C9—63no—
107C33—41no—
108C33—43no—
109C33—83no—
110C33—81no—
111C33—122no—
112C33—121no—
113C33—242no—
114C33—241no—
115C33D3×A411yescharacteristic
116C3×C9—21no—
117C3×C9—31no—
118C3×C9—61no—
119C3×C9—83no—
120C3×C9—242no—
121C3×C9—241no—
122C3×C9C2×C3×A411yescharacteristic, complemented
123C23×C3—271no—
124C22×D3—91no—
125C22×D3—91no—
126C22×D3—92no—
127C2×A4—273no—
128C2×C32—31no—
129C2×C32—32no—
130C2×C32—31no—
131C2×C32—31no—
132C2×C32—61no—
133C2×C32—62no—
134C2×C32—61no—
135C2×C32—1081no—
136C3⋊D3—31no—
137C3⋊D3—91no—
138C3×D3—92no—
139C3×D3—91no—
140C3×D3—91no—
141C3×D3—272no—
142C3×D3—271no—
143C3×D3—271no—
144C3×D3—363no—
145C3×D3—366no—
146C3×D3—363no—
147C2×C9—33no—
148C2×C9—63no—
149D9—91no—
150D9—93no—
151C22×C3—21no—
152C22×C3—21no—
153C22×C3—22no—
154C22×C3—811no—
155C22×C3—811no—
156C22×C3#416911yescharacteristic, complemented
157C22×C3C32×D911yescharacteristic
158C22×C3C3×(C3⋊D3)⋊C311yescharacteristic
159C22×C3C3×AGL(1,ℤ/9)12yes—
160C2×D3—271no—
161C2×D3—272no—
162C2×D3—271no—
163C2×D3—271no—
164C2×D3—272no—
165C2×D3—271no—
166A4—33no—
167A4—63no—
168C32—22no—
169C32—21no—
170C32—21no—
171C32—43no—
172C32—83no—
173C32—121no—
174C32—126no—
175C32—123no—
176C32—241no—
177C32—246no—
178C32—243no—
179C32—242no—
180C32—241no—
181C32D9⋊A412yes—
182C32A4×D911yescharacteristic
183C32(C3⋊D3)⋊A411yescharacteristic
184C32C3×D3×A411yescharacteristic
185C9—31no—
186C9—61no—
187C9—243no—
188C23—271noSylow
189C2×C3—31no—
190C2×C3—32no—
191C2×C3—31no—
192C2×C3—31no—
193C2×C3—62no—
194C2×C3—61no—
195C2×C3—61no—
196C2×C3—271no—
197C2×C3—811no—
198C2×C3—1083no—
199D3—92no—
200D3—91no—
201D3—91no—
202D3—272no—
203D3—271no—
204D3—271no—
205C22—811no—
206C22—811no—
207C22C3×#416911yescharacteristic, complemented
208C3—22no—
209C3—21no—
210C3—21no—
211C3—123no—
212C3—243no—
213C3#1061977011yescharacteristic, direct product factor
214C3C3×D9⋊A412yes—
215C3C3×A4×D911yescharacteristic
216C3C3×(C3⋊D3)⋊A411yescharacteristic
217C2—31no—
218C2—271no—
219C2—811no—
subgroupG/H
center, hypercenterC3#10619770
commutator, cosocle, hypocenterC22×C3×C9C2×C32
FrattiniC32C3×D3×A4
FittingC22×C32×C9C2×C3
socleC22×C33C3×D3
LCSG ▷ C22×C3×C9
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×(C3×A4)⋊C9C2semidirect
3. C22×C3×C3⋊D9C3semidirect
4. #10619770C3direct (N × H)
7. C22×C32×C9C2×C3semidirect
12. (C3×A4)⋊C9C2×C3semidirect
19. C22×C3⋊D9C32semidirect
24. C3×C3⋊D9A4semidirect
35. C32×A4D9semidirect
40. C22×C3×C9C2×C32semidirect
50. C32×C9C2×A4semidirect
74. C3⋊D9C3×A4semidirect
101. C3×A4C3×D9semidirect
122. C3×C9C2×C3×A4semidirect
156. C22×C3#4169semidirect
207. C22C3×#4169semidirect
213. C3#10619770direct (N × H)

Maximal subgroups

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

subgroupindex
C3×(C3×A4)⋊C92
C3×A4×C3⋊D33
C22×C3×C3⋊D93
#106197703
C3×#41694