Finite Group Databasebeta

← C2×#10620155 #13049716

Subgroups — C2×#10620155 #13049716

Order 1296.

1140 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1140 conjugacy classes of subgroups — too many to draw. Only its 203 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
1C22×C32×C3⋊D3C211yesmaximal, characteristic
2C2×C3×C3⋊(C3⋊Dic3)C212yesmaximal, complemented
3#10620155C214yesmaximal, direct product factor
4C2×#6294—34nomaximal
5C2×D3×C3⋊Dic3—32nomaximal
6C22×C34C2211yescharacteristic
7C2×C32×C3⋊D3C414yescomplemented
8C2×C32×C3⋊D3C2212yes—
9C3×C3⋊(C3⋊Dic3)C2214yescomplemented
10C22×C3×C3⋊D3D314yes—
11C22×C32×D3—32no—
12C22×C32×D3—61no—
13C2×C3⋊(C3⋊Dic3)D312yescomplemented
14C2×C3×C3⋊Dic3—32no—
15C2×C3×C3⋊Dic3—38no—
16C2×C3×C3⋊Dic3—68no—
17#6294—316no—
18D3×C3⋊Dic3—38no—
19C2×C34C2×C412yescomplemented
20C2×C34C2311yescharacteristic
21C32×C3⋊D3C2×C414yescomplemented
22C22×C3⋊Dic3—91no—
23C2×#624—91no—
24C2×D3×Dic3—98no—
25C22×C33—28no—
26C22×C33—21no—
27C22×C33—44no—
28C22×C33C2×D312yes—
29C22×C33C2×D314yes—
30C2×C3×C3⋊D3Dic3116yescomplemented
31C2×C3×C3⋊D3C2×D318yes—
32C2×C32×D3—38no—
33C2×C32×D3—34no—
34C2×C32×D3—64no—
35C2×C32×D3—62no—
36C3⋊(C3⋊Dic3)C2×D314yescomplemented
37C3×C3⋊Dic3—34no—
38C3×C3⋊Dic3—316no—
39C3×C3⋊Dic3—616no—
40C34C22×C411yescharacteristic, complemented, Sylow
41C23×C32—91no—
42C22×C3⋊D3C3⋊D311yescharacteristic
43C22×C3×D3—38no—
44C22×C3×D3—64no—
45C2×C3⋊Dic3—32no—
46C2×C3⋊Dic3—38no—
47C2×C3⋊Dic3—68no—
48C2×C3⋊Dic3—94no—
49C2×C3×Dic3—98no—
50C2×C3×Dic3—92no—
51C2×C3×Dic3—188no—
52#624—94no—
53D3×Dic3—932no—
54C2×C33—216no—
55C2×C33—22no—
56C2×C33—28no—
57C2×C33—21no—
58C2×C33—48no—
59C2×C33—44no—
60C2×C33C4×D314yescomplemented
61C2×C33C2×Dic318yescomplemented
62C2×C33C22×D312yes—
63C2×C33C22×D314yes—
64C3×C3⋊D3C2×Dic3116yescomplemented
65C32×D3—38no—
66C32×D3—64no—
67C22×Dic3—274no—
68C2×C4×D3—272no—
69C22×C32—28no—
70C22×C32—28no—
71C22×C32—24no—
72C22×C32—44no—
73C22×C32—412no—
74C22×C32—44no—
75C22×C32—94no—
76C22×C32—92no—
77C22×C32D3218yes—
78C22×C32D3211yescharacteristic
79C22×C32C2×C3⋊D311yescharacteristic
80C2×C3⋊D3C3⋊Dic314yescomplemented
81C2×C3⋊D3C2×C3⋊D312yes—
82C2×C3×D3—332no—
83C2×C3×D3—316no—
84C2×C3×D3—616no—
85C2×C3×D3—68no—
86C3⋊Dic3—34no—
87C3⋊Dic3—316no—
88C3⋊Dic3—616no—
89C3×Dic3—916no—
90C3×Dic3—94no—
91C3×Dic3—1816no—
92C33—28no—
93C33—21no—
94C33—44no—
95C33C2×C4×D312yescomplemented
96C33C22×Dic314yescomplemented
97C23×C3—94no—
98C22×D3—32no—
99C22×D3—61no—
100C2×C3×C4—272no—
101C2×Dic3—92no—
102C2×Dic3—98no—
103C2×Dic3—188no—
104C2×Dic3—2716no—
105C4×D3—278no—
106C2×C32—216no—
107C2×C32—28no—
108C2×C32—216no—
109C2×C32—28no—
110C2×C32—28no—
111C2×C32—24no—
112C2×C32—48no—
113C2×C32—44no—
114C2×C32—412no—
115C2×C32—424no—
116C2×C32—48no—
117C2×C32—44no—
118C2×C32—94no—
119C2×C32D3×Dic3116yescomplemented
120C2×C32#62412yescomplemented
121C2×C32C2×C3⋊Dic312yescomplemented
122C2×C32C2×D3218yes—
123C2×C32C2×D3211yescharacteristic
124C2×C32C22×C3⋊D311yescharacteristic
125C3⋊D3C2×C3⋊Dic314yescomplemented
126C3×D3—332no—
127C3×D3—616no—
128C22×C4—811noSylow
129C22×C3—28no—
130C22×C3—21no—
131C22×C3—44no—
132C22×C3—916no—
133C22×C3—98no—
134C22×C3D3×C3⋊D312yes—
135C22×C3#111314yes—
136C2×D3—38no—
137C2×D3—34no—
138C2×D3—64no—
139C2×D3—62no—
140C3×C4—274no—
141Dic3—94no—
142Dic3—916no—
143Dic3—1816no—
144C32—28no—
145C32—28no—
146C32—24no—
147C32—44no—
148C32—412no—
149C32—44no—
150C32C2×D3×Dic318yescomplemented
151C32C2×#62411yescharacteristic, complemented
152C32C22×C3⋊Dic311yescharacteristic, complemented
153C23—91no—
154C2×C4—272no—
155C2×C4—814no—
156C2×C3—28no—
157C2×C3—21no—
158C2×C3—22no—
159C2×C3—216no—
160C2×C3—44no—
161C2×C3—48no—
162C2×C3—916no—
163C2×C3D3×C3⋊Dic314yescomplemented
164C2×C3#629418yescomplemented
165C2×C3C2×D3×C3⋊D312yes—
166C2×C3C2×#111314yes—
167D3—38no—
168D3—64no—
169C22—92no—
170C22—94no—
171C22C3⋊#111311yescharacteristic
172C4—274no—
173C3—21no—
174C3—28no—
175C3—44no—
176C3C2×D3×C3⋊Dic312yescomplemented
177C3C2×#629414yescomplemented
178C2—94no—
179C2#1062015512yesdirect product factor
180C2C2×C3⋊#111311yescharacteristic
subgroupG/H
center, hypercenterC22C3⋊#1113
commutator, hypocenterC34C22×C4
FrattiniC2C2×C3⋊#1113
Fitting, socleC22×C34C22
prime radicalC22×C32×C3⋊D3C2
cosocleC2×C34C23
LCSG ▷ C34
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. C2×C3×C3⋊(C3⋊Dic3)C2semidirect
3. #10620155C2direct (N × H)
7. C2×C32×C3⋊D3C4semidirect
9. C3×C3⋊(C3⋊Dic3)C22semidirect
13. C2×C3⋊(C3⋊Dic3)D3semidirect
19. C2×C34C2×C4semidirect
21. C32×C3⋊D3C2×C4semidirect
30. C2×C3×C3⋊D3Dic3semidirect
36. C3⋊(C3⋊Dic3)C2×D3semidirect
40. C34C22×C4semidirect
60. C2×C33C4×D3semidirect
61. C2×C33C2×Dic3semidirect
64. C3×C3⋊D3C2×Dic3semidirect
80. C2×C3⋊D3C3⋊Dic3semidirect
95. C33C2×C4×D3semidirect
96. C33C22×Dic3semidirect
119. C2×C32D3×Dic3semidirect
120. C2×C32#624semidirect
121. C2×C32C2×C3⋊Dic3semidirect
125. C3⋊D3C2×C3⋊Dic3semidirect
150. C32C2×D3×Dic3semidirect
151. C32C2×#624semidirect
152. C32C22×C3⋊Dic3semidirect
163. C2×C3D3×C3⋊Dic3semidirect
164. C2×C3#6294semidirect
176. C3C2×D3×C3⋊Dic3semidirect
177. C3C2×#6294semidirect
179. C2#10620155direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×C3⋊D32
C2×C3×C3⋊(C3⋊Dic3)2
#106201552
C2×#62943
C2×D3×C3⋊Dic33