Finite Group Databasebeta

← #13048745

Subgroups — #13048745

Order 1296.

424 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 68 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×#66431C212yesmaximal, complemented
2C4×C9×C3⋊D3C211yesmaximal, characteristic, complemented
3C3×C4⋊(C3⋊D9)C212yesmaximal, complemented
4#10619897C212yesmaximal, complemented
5C4⋊#1113—31nomaximal
6D3×D36—32nomaximal
7C2×C9×C3⋊D3C2211yescharacteristic
8C2×C3×C3⋊D9C2214yescomplemented
9#66431—24no—
10C32×C4×C9C2211yescharacteristic, complemented
11C9×C3⋊Dic3C2211yescharacteristic, complemented
12C2×#1113—32no—
13C3×C4⋊(C3⋊D3)—32no—
14C3×C4×C3⋊D3D311yescharacteristic
15#6295—32no—
16C2×D3×D9—34no—
17C4⋊(C3⋊D9)D312yescomplemented
18C4×D3×C9—32no—
19C4×D3×C9—61no—
20C3×D36—32no—
21C3×D36—62no—
22#6192—34no—
23C2×C32×C9C2311yescharacteristic
24C9×C3⋊D3D412yescomplemented
25C3×C3⋊D9—24no—
26#3802—91no—
27D3×D12—92no—
28C2×D36—91no—
29C2×C3×C3⋊D3—34no—
30C2×C3×C3⋊D3C2×D311yescharacteristic
31#1113—64no—
32C33×C4C2×D311yescharacteristic
33C3×C3⋊Dic3C2×D311yescharacteristic
34C2×C3⋊D9C2×D314yescomplemented
35C2×D3×C9—32no—
36C2×D3×C9—61no—
37C2×C3×D9—34no—
38C2×C3×D9—64no—
39D3×D9—68no—
40C3×C4×C9—22no—
41C3×C4×C9—21no—
42C3×C4×C9—41no—
43C3×C4×C9C2×D312yescomplemented
44C9×Dic3—32no—
45C9×Dic3—61no—
46C32×C9C2×D411yescharacteristic, complemented, Sylow
47C2×D32—94no—
48C2×D32—92no—
49C4⋊(C3⋊D3)—32no—
50C4×C3⋊D3D911yescharacteristic, complemented
51C3×D12—92no—
52C3×D12—92no—
53C3×D12—182no—
54C3×C4×D3—32no—
55C3×C4×D3—61no—
56#626—94no—
57#625—92no—
58C22×D9—92no—
59C2×C4×C9—91no—
60D36—32no—
61D36—62no—
62D36—92no—
63C2×C33C22×D311yescharacteristic
64C3×C3⋊D3—64no—
65C3×C3⋊D3D1212yes—
66C2×C3×C9—22no—
67C2×C3×C9—21no—
68C2×C3×C9—41no—
69C2×C3×C9C22×D312yes—
70C3⋊D9—24no—
71D3×C9—34no—
72D3×C9—62no—
73C3×D9—64no—
74C3×D9—124no—
75D3×D4—272no—
76C2×D12—271no—
77C2×C3⋊D3—34no—
78C2×C3⋊D3C2×D911yescharacteristic
79C2×C3×D3—32no—
80C2×C3×D3—61no—
81C2×C3×D3—94no—
82C2×C3×D3—94no—
83C2×C3×D3—184no—
84D32—188no—
85D32—184no—
86C32×C4—22no—
87C32×C4—21no—
88C32×C4—41no—
89C32×C4C2×D911yescharacteristic, complemented
90C32×C4D3212yes—
91C3⋊Dic3C2×D911yescharacteristic, complemented
92C3×Dic3—32no—
93C3×Dic3—61no—
94C22×C9—91no—
95C2×D9—34no—
96C2×D9—64no—
97C2×D9—184no—
98C4×C9—22no—
99C4×C9—41no—
100C4×C9—91no—
101C4×C9D3211yescharacteristic, complemented
102C33C2×D1211yescharacteristic
103C3×C9—22no—
104C3×C9—21no—
105C3×C9—41no—
106C3×C9D3×D412yescomplemented
107C22×D3—274no—
108C22×D3—272no—
109C3×D4—272no—
110C2×C3×C4—91no—
111#67—274no—
112D12—92no—
113D12—92no—
114D12—182no—
115D12—272no—
116C4×D3—32no—
117C4×D3—61no—
118C2×C32—22no—
119C2×C32—21no—
120C2×C32—41no—
121C2×C32C22×D911yescharacteristic
122C2×C32C2×D3212yes—
123C3⋊D3—64no—
124C3⋊D3D3612yescomplemented
125C3×D3—34no—
126C3×D3—62no—
127C3×D3—184no—
128C3×D3—184no—
129C3×D3—364no—
130C2×C9—22no—
131C2×C9—41no—
132C2×C9—92no—
133C2×C9C2×D3211yescharacteristic
134D9—64no—
135D9—124no—
136C2×D4—811noSylow
137C22×C3—91no—
138C22×C3—274no—
139C2×D3—32no—
140C2×D3—61no—
141C2×D3—94no—
142C2×D3—94no—
143C2×D3—184no—
144C2×D3—548no—
145C2×D3—544no—
146C3×C4—21no—
147C3×C4—22no—
148C3×C4—41no—
149C3×C4—91no—
150C3×C4D3×D912yescomplemented
151C3×C4#111311yescharacteristic
152Dic3—32no—
153Dic3—61no—
154C32—22no—
155C32—21no—
156C32—41no—
157C32C2×D3611yescharacteristic, complemented
158C32D3×D1212yes—
159C9—22no—
160C9—41no—
161C9#380211yescharacteristic, complemented
162C23—812no—
163D4—272no—
164D4—812no—
165C2×C4—91no—
166C2×C3—21no—
167C2×C3—22no—
168C2×C3—41no—
169C2×C3—92no—
170C2×C3—544no—
171C2×C3C2×D3×D912yes—
172C2×C3C2×#111311yescharacteristic
173D3—34no—
174D3—62no—
175D3—184no—
176D3—184no—
177D3—364no—
178C22—91no—
179C22—274no—
180C22—1624no—
181C4—91no—
182C4#6643111yescharacteristic, complemented
183C3—21no—
184C3—22no—
185C3—41no—
186C3D3×D3612yescomplemented
187C3C4⋊#111311yescharacteristic
188C2—92no—
189C2—544no—
190C2C2×#6643111yescharacteristic
subgroupG/H
centerC2C2×#66431
commutator, cosocleC2×C32×C9C23
FrattiniC2×C3C2×#1113
FittingC32×C4×C9C22
socleC2×C33C22×D3
hypercenterC4#66431
hypocenterC32×C9C2×D4
LCSG ▷ C2×C32×C9 ▷ C32×C9
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C2×#66431C2semidirect
2. C4×C9×C3⋊D3C2semidirect
3. C3×C4⋊(C3⋊D9)C2semidirect
4. #10619897C2semidirect
8. C2×C3×C3⋊D9C22semidirect
10. C32×C4×C9C22semidirect
11. C9×C3⋊Dic3C22semidirect
17. C4⋊(C3⋊D9)D3semidirect
24. C9×C3⋊D3D4semidirect
34. C2×C3⋊D9C2×D3semidirect
43. C3×C4×C9C2×D3semidirect
46. C32×C9C2×D4semidirect
50. C4×C3⋊D3D9semidirect
89. C32×C4C2×D9semidirect
91. C3⋊Dic3C2×D9semidirect
101. C4×C9D32semidirect
106. C3×C9D3×D4semidirect
124. C3⋊D3D36semidirect
150. C3×C4D3×D9semidirect
157. C32C2×D36semidirect
161. C9#3802semidirect
182. C4#66431semidirect
186. C3D3×D36semidirect

Maximal subgroups

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

subgroupindex
C2×#664312
C4×C9×C3⋊D32
C3×C4⋊(C3⋊D9)2
#106198972
C4⋊#11133
D3×D363