Finite Group Databasebeta

← C3×#10619754 #14518050

Subgroups — C3×#10619754 #14518050

Order 1944.

382 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 44 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
2C32×C3⋊S4—31nomaximal
3C32×(C22⋊C9)⋊C2—32nomaximal
4C32×#611—31nomaximal
5#10619754C311yesmaximal, characteristic, direct product factor
6C3×#4181—41nomaximal
7C33×A4D311yescharacteristic
8C22×C32×C9D311yescharacteristic, complemented
9C2×C32×D9—31no—
10C32×C22⋊C9D312yescomplemented
11C32×Dic9—31no—
12(C3×A4)⋊C9—21no—
13(C3×A4)⋊C9—21no—
14(C3×A4)⋊C9—22no—
15(C3×A4)⋊C9C2×C311yescharacteristic, complemented
16C3×C32⋊C9—41noSylow
17C3×C3⋊S4—33no—
18C3×C3⋊S4—31no—
19C32×S4—93no—
20C32×#67—91no—
21C3×(C22⋊C9)⋊C2—36no—
22C3×(C22⋊C9)⋊C2—32no—
23C3×#611—33no—
24C3×#611—31no—
25C32×C3⋊D3—121no—
26C2×C32×C9—31no—
27C32×D9—61no—
28C32×D9—122no—
29#4181—41no—
30C22×C33C3⋊D311yescharacteristic
31C2×C32×D3—91no—
32C32×A4—21no—
33C32×A4—23no—
34C32×A4—33no—
35C32×A4—63no—
36C32×A4D913yescomplemented
37C32×A4C3×D311yescharacteristic
38C32×Dic3—91no—
39C22×C3×C9—21no—
40C22×C3×C9—33no—
41C22×C3×C9C3×D311yescharacteristic, complemented
42C2×C3×D9—33no—
43C2×C3×D9—31no—
44C3×C22⋊C9—22no—
45C3×C22⋊C9—36no—
46C3×C22⋊C9C3×D312yescomplemented
47C3×Dic9—33no—
48C3×Dic9—31no—
49C34—41no—
50C32×C9—42no—
51C32×C9S411yescharacteristic, complemented
52C32⋊C9—41no—
53C32⋊C9—82no—
54C32⋊C9—81no—
55C32⋊C9—81no—
56C3⋊S4—31no—
57C3×S4—99no—
58C3×S4—93no—
59C32×D4—271no—
60C3×#67—93no—
61C3×#67—91no—
62(C22⋊C9)⋊C2—32no—
63#611—31no—
64C2×C33—31no—
65C3×C3⋊D3—121no—
66C3×C3⋊D3—123no—
67C32×D3—181no—
68C32×D3—363no—
69C2×C3×C9—33no—
70C2×C3×C9—31no—
71C2×C3×C9—61no—
72C2×C3×C9—63no—
73C3×D9—63no—
74C3×D9—61no—
75C3×D9—122no—
76C3×D9—126no—
77C22×C32—23no—
78C22×C32—21no—
79C22×C32—271no—
80C22×C32C3⋊D911yescharacteristic
81C22×C32#27213yes—
82C22×C32C3×C3⋊D311yescharacteristic
83C2×C3×D3—93no—
84C2×C3×D3—91no—
85C3×A4—23no—
86C3×A4—31no—
87C3×A4—39no—
88C3×A4—61no—
89C3×A4—69no—
90C3×A4—62no—
91C3×A4—61no—
92C3×A4C3×D913yescomplemented
93C32×C4—271no—
94C3×Dic3—93no—
95C3×Dic3—91no—
96C22×C9—31no—
97C22×C9—61no—
98C2×D9—31no—
99C22⋊C9—32no—
100C22⋊C9—62no—
101Dic9—31no—
102C33—41no—
103C33—43no—
104C33—83no—
105C33—81no—
106C33—123no—
107C33—243no—
108C33C3⋊S411yescharacteristic
109C3×C9—21no—
110C3×C9—33no—
111C3×C9—42no—
112C3×C9—82no—
113C3×C9—126no—
114C3×C9C3×S411yescharacteristic, complemented
115S4—93no—
116C3×D4—273no—
117C3×D4—271no—
118#67—91no—
119C2×C32—31no—
120C2×C32—33no—
121C2×C32—31no—
122C2×C32—63no—
123C2×C32—61no—
124C2×C32—541no—
125C3⋊D3—121no—
126C3×D3—183no—
127C3×D3—181no—
128C3×D3—363no—
129C3×D3—369no—
130C2×C9—31no—
131C2×C9—61no—
132C2×C9—63no—
133D9—61no—
134D9—122no—
135C22×C3—23no—
136C22×C3—21no—
137C22×C3—273no—
138C22×C3—271no—
139C22×C3#418113yescomplemented
140C22×C3C3×C3⋊D911yescharacteristic
141C22×C3C3×#27211yescharacteristic
142C2×D3—91no—
143A4—33no—
144A4—63no—
145C3×C4—273no—
146C3×C4—271no—
147Dic3—91no—
148C32—23no—
149C32—21no—
150C32—43no—
151C32—83no—
152C32—121no—
153C32—129no—
154C32—241no—
155C32—249no—
156C32—242no—
157C32—241no—
158C32C9⋊S411yescharacteristic
159C32#625813yes—
160C32C3×C3⋊S411yescharacteristic
161C9—31no—
162C9—61no—
163C9—122no—
164C9—242no—
165D4—271noSylow
166C2×C3—33no—
167C2×C3—31no—
168C2×C3—31no—
169C2×C3—63no—
170C2×C3—61no—
171C2×C3—543no—
172C2×C3—541no—
173D3—181no—
174D3—363no—
175C22—271no—
176C22C3×#418111yescharacteristic, complemented
177C4—271no—
178C3—23no—
179C3—21no—
180C3—123no—
181C3—243no—
182C3#1061975413yesdirect product factor
183C3C3×C9⋊S411yescharacteristic
184C3C3×#625811yescharacteristic
185C2—31no—
186C2—541no—
subgroupG/H
center, hypercenterC32C9⋊S4
commutator, cosocle, hypocenter(C3×A4)⋊C9C2×C3
FrattiniC32C3×C3⋊S4
FittingC22×C32×C9D3
socleC22×C33C3⋊D3
LCSG ▷ (C3×A4)⋊C9
UCSC1 ◁ C32

Complements

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

NH ≅ G/Ntype
1. C3×(C3×A4)⋊C9C2semidirect
5. #10619754C3direct (N × H)
8. C22×C32×C9D3semidirect
10. C32×C22⋊C9D3semidirect
15. (C3×A4)⋊C9C2×C3semidirect
36. C32×A4D9semidirect
41. C22×C3×C9C3×D3semidirect
46. C3×C22⋊C9C3×D3semidirect
51. C32×C9S4semidirect
92. C3×A4C3×D9semidirect
114. C3×C9C3×S4semidirect
139. C22×C3#4181semidirect
176. C22C3×#4181semidirect
182. C3#10619754direct (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
C32×C3⋊S43
C32×(C22⋊C9)⋊C23
C32×#6113
#106197543
C3×#41814