Finite Group Databasebeta

← C3×#10619870 #14518648

Subgroups — C3×#10619870 #14518648

Order 1944.

668 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C2×C3×C3⋊(C3⋊D9)C211yesmaximal, characteristic
2C3×C9×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C33×Dic9C211yesmaximal, characteristic, complemented
4C3×#6289—31nomaximal
5#10619870C311yesmaximal, characteristic, direct product factor
6C3×(C3⋊D9)⋊C4—34nomaximal
7C2×C33×C9C2211yescharacteristic
8C3×C3⋊(C3⋊D9)C412yescomplemented
9C2×C3×C3⋊(C3⋊D3)—31no—
10C32×C3⋊Dic3D311yescharacteristic
11C33×Dic3—31no—
12C2×C3⋊(C3⋊D9)C2×C311yescharacteristic
13C2×C3×C3⋊D9—34no—
14C2×C3×C3⋊D9—64no—
15C9×C3⋊Dic3—21no—
16C9×C3⋊Dic3C2×C311yescharacteristic, complemented
17C3×C9×Dic3—34no—
18C32×Dic9—24no—
19C32×Dic9D314yescomplemented
20C32×Dic9C2×C311yescharacteristic, complemented
21C33×C9C2×C411yescharacteristic, complemented, Sylow
22C3×C4×C3⋊D3—91no—
23#6289—31no—
24C3×#624—94no—
25C3×C4×D9—91no—
26(C3⋊D9)⋊C4—34no—
27C2×C34C2×D311yescharacteristic
28C3×C3⋊(C3⋊D3)—32no—
29C2×C32×C9—24no—
30C2×C32×C9—21no—
31C2×C32×C9—24no—
32C2×C32×C9—44no—
33C2×C32×C9C2×D314yes—
34C2×C32×C9C22×C311yescharacteristic
35C3⋊(C3⋊D9)C3×C412yescomplemented
36C3×C3⋊D9—38no—
37C3×C3⋊D9—68no—
38C2×C3⋊(C3⋊D3)—31no—
39C2×C3×C3⋊D3—91no—
40C2×C3×C3⋊D3—94no—
41C2×C3×C3⋊D3—184no—
42C33×C4—91no—
43C3×C3⋊Dic3—21no—
44C3×C3⋊Dic3D911yescharacteristic, complemented
45C3×C3⋊Dic3C3×D311yescharacteristic
46C32×Dic3—34no—
47C32×Dic3—34no—
48C32×Dic3—31no—
49C32×Dic3—64no—
50C2×C3⋊D9—34no—
51C2×C3⋊D9—64no—
52C2×C3×D9—91no—
53C2×C3×D9—184no—
54C3×C4×C9—91no—
55C9×Dic3—34no—
56C9×Dic3—64no—
57C3×Dic9—24no—
58C3×Dic9C3×D314yescomplemented
59C3×Dic9C3⋊D311yescharacteristic, complemented
60C34C4×D311yescharacteristic
61C32×C9—24no—
62C32×C9—21no—
63C32×C9—24no—
64C32×C9—44no—
65C32×C9C4×D314yescomplemented
66C32×C9C2×C3×C411yescharacteristic, complemented
67C4×C3⋊D3—91no—
68C3×C4×D3—271no—
69C3×C4×D3—274no—
70#624—94no—
71C4×D9—91no—
72C2×C33—24no—
73C2×C33—21no—
74C2×C33—24no—
75C2×C33—44no—
76C2×C33C2×D911yescharacteristic
77C2×C33D3214yes—
78C2×C33C2×C3×D311yescharacteristic
79C3⋊(C3⋊D3)—32no—
80C3×C3⋊D3—92no—
81C3×C3⋊D3—98no—
82C3×C3⋊D3—188no—
83C2×C3×C9—24no—
84C2×C3×C9—24no—
85C2×C3×C9—24no—
86C2×C3×C9—24no—
87C2×C3×C9—44no—
88C2×C3×C9—412no—
89C2×C3×C9—44no—
90C2×C3×C9C2×C3×D314yes—
91C2×C3×C9C2×C3⋊D311yescharacteristic
92C3⋊D9—38no—
93C3⋊D9—68no—
94C3×D9—92no—
95C3×D9—188no—
96C2×C3⋊D3—91no—
97C2×C3⋊D3—94no—
98C2×C3⋊D3—184no—
99C2×C3×D3—274no—
100C2×C3×D3—271no—
101C2×C3×D3—544no—
102C32×C4—91no—
103C32×C4—94no—
104C32×C4—91no—
105C32×C4—184no—
106C3⋊Dic3C3×D911yescharacteristic, complemented
107C3×Dic3—34no—
108C3×Dic3—34no—
109C3×Dic3—34no—
110C3×Dic3—31no—
111C3×Dic3—64no—
112C3×Dic3—64no—
113C2×D9—91no—
114C2×D9—184no—
115C4×C9—91no—
116C4×C9—181no—
117Dic9C3×C3⋊D311yescharacteristic, complemented
118C33—24no—
119C33—21no—
120C33—24no—
121C33—44no—
122C33C4×D911yescharacteristic, complemented
123C33#62414yes—
124C33C3×C4×D311yescharacteristic
125C3×C9—24no—
126C3×C9—24no—
127C3×C9—24no—
128C3×C9—24no—
129C3×C9—44no—
130C3×C9—412no—
131C3×C9—44no—
132C3×C9C3×C4×D314yescomplemented
133C3×C9C4×C3⋊D311yescharacteristic, complemented
134C2×C3×C4—811no—
135C4×D3—271no—
136C4×D3—274no—
137C2×C32—24no—
138C2×C32—24no—
139C2×C32—24no—
140C2×C32—24no—
141C2×C32—24no—
142C2×C32—44no—
143C2×C32—412no—
144C2×C32—44no—
145C2×C32D3×D914yes—
146C2×C32C2×C3×D911yescharacteristic
147C2×C32C3×D3214yes—
148C2×C32D3×C3⋊D311yescharacteristic
149C3⋊D3—92no—
150C3⋊D3—98no—
151C3⋊D3—188no—
152C3×D3—278no—
153C3×D3—272no—
154C3×D3—548no—
155C2×C9—24no—
156C2×C9—21no—
157C2×C9—44no—
158C2×C9C2×C3×C3⋊D311yescharacteristic
159D9—92no—
160D9—188no—
161C22×C3—811no—
162C2×D3—274no—
163C2×D3—271no—
164C2×D3—544no—
165C3×C4—94no—
166C3×C4—91no—
167C3×C4—91no—
168C3×C4—91no—
169C3×C4—181no—
170C3×C4—184no—
171Dic3—34no—
172Dic3—31no—
173C32—24no—
174C32—24no—
175C32—24no—
176C32—24no—
177C32—24no—
178C32—44no—
179C32—412no—
180C32—44no—
181C32(C3⋊D9)⋊C414yescomplemented
182C32C3×C4×D911yescharacteristic, complemented
183C32C3×#62414yes—
184C32#628911yescharacteristic
185C9—24no—
186C9—21no—
187C9—44no—
188C9C3×C4×C3⋊D311yescharacteristic, complemented
189C2×C4—811noSylow
190C2×C3—24no—
191C2×C3—21no—
192C2×C3—24no—
193C2×C3—44no—
194C2×C3—812no—
195C2×C3C3×D3×D914yes—
196C2×C3D9×C3⋊D311yescharacteristic
197C2×C3C3×D3×C3⋊D311yescharacteristic
198D3—278no—
199D3—272no—
200D3—548no—
201C22—811no—
202C4—91no—
203C4—91no—
204C3—24no—
205C3—24no—
206C3—21no—
207C3—44no—
208C3C3×(C3⋊D9)⋊C414yescomplemented
209C3#1061987011yescharacteristic, direct product factor
210C3C3×#628911yescharacteristic
211C2—812no—
212C2C3×D9×C3⋊D311yescharacteristic
subgroupG/H
center, hypercenterC2×C3D9×C3⋊D3
commutator, hypocenterC32×C9C2×C3×C4
FrattiniC2×C3C3×D3×C3⋊D3
FittingC2×C33×C9C22
socleC2×C34C2×D3
prime radicalC2×C3×C3⋊(C3⋊D9)C2
cosocleC2×C32×C9C22×C3
LCSG ▷ C32×C9
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
2. C3×C9×C3⋊Dic3C2semidirect
3. C33×Dic9C2semidirect
5. #10619870C3direct (N × H)
8. C3×C3⋊(C3⋊D9)C4semidirect
16. C9×C3⋊Dic3C2×C3semidirect
19. C32×Dic9D3semidirect
20. C32×Dic9C2×C3semidirect
21. C33×C9C2×C4semidirect
35. C3⋊(C3⋊D9)C3×C4semidirect
44. C3×C3⋊Dic3D9semidirect
58. C3×Dic9C3×D3semidirect
59. C3×Dic9C3⋊D3semidirect
65. C32×C9C4×D3semidirect
66. C32×C9C2×C3×C4semidirect
106. C3⋊Dic3C3×D9semidirect
117. Dic9C3×C3⋊D3semidirect
122. C33C4×D9semidirect
132. C3×C9C3×C4×D3semidirect
133. C3×C9C4×C3⋊D3semidirect
181. C32(C3⋊D9)⋊C4semidirect
182. C32C3×C4×D9semidirect
188. C9C3×C4×C3⋊D3semidirect
208. C3C3×(C3⋊D9)⋊C4semidirect
209. C3#10619870direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C3⋊(C3⋊D9)2
C3×C9×C3⋊Dic32
C33×Dic92
C3×#62893
#106198703
C3×(C3⋊D9)⋊C43