Finite Group Databasebeta

← #89049

Subgroups — #89049

Order 432.

290 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 51 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×C3×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#1113C211yesmaximal, characteristic, complemented
3C3×#638C212yesmaximal, complemented
4#6295C212yesmaximal, complemented
5#6294C211yesmaximal, characteristic, complemented
6#3811—31nomaximal
7D3×#67—32nomaximal
8C22×C33C2211yescharacteristic, complemented
9C2×C3×C3⋊D3—22no—
10C2×C3×C3⋊D3C2211yescharacteristic
11C2×C3×C3⋊D3C2211yescharacteristic, complemented
12C2×C3×C3⋊D3C2212yescomplemented
13#1113—22no—
14C3×C3⋊Dic3C2212yescomplemented
15C22×C3⋊D3D311yescharacteristic, complemented
16C22×C3×D3—32no—
17C22×C3×D3—61no—
18C2×D32—31no—
19C2×D32—32no—
20#638D312yescomplemented
21C3×#67—32no—
22C3×#67—32no—
23C3×#67—62no—
24#626—32no—
25#626—32no—
26#625—32no—
27#624—31no—
28D3×Dic3—32no—
29C2×C33—21no—
30C2×C33C2311yescharacteristic
31C3×C3⋊D3—21no—
32C3×C3⋊D3—22no—
33C3×C3⋊D3D412yescomplemented
34C2×#67—91no—
35D3×D4—92no—
36C22×C32—21no—
37C22×C32—22no—
38C22×C32—41no—
39C22×C32C2×D311yescharacteristic, complemented
40C22×C32C2×D312yescomplemented
41C2×C3⋊D3—22no—
42C2×C3⋊D3C2×D311yescharacteristic
43C2×C3⋊D3C2×D311yescharacteristic, complemented
44C2×C3⋊D3C2×D312yescomplemented
45C2×C3×D3—32no—
46C2×C3×D3—32no—
47C2×C3×D3—32no—
48C2×C3×D3—32no—
49C2×C3×D3—61no—
50C2×C3×D3—61no—
51C2×C3×D3—62no—
52C2×C3×D3—64no—
53C2×C3×D3—64no—
54D32—64no—
55D32—62no—
56C3⋊Dic3C2×D312yescomplemented
57C3×Dic3—32no—
58C3×Dic3—32no—
59C3×Dic3—62no—
60C33C2×D411yescharacteristic, complemented, Sylow
61C23×C3—91no—
62C22×D3—32no—
63C22×D3—61no—
64C22×D3—92no—
65C22×D3—91no—
66C3×D4—92no—
67#67—32no—
68#67—32no—
69#67—62no—
70#67—92no—
71#67—92no—
72C2×Dic3—91no—
73D12—92no—
74C4×D3—92no—
75C2×C32—21no—
76C2×C32—22no—
77C2×C32—22no—
78C2×C32—22no—
79C2×C32—21no—
80C2×C32—41no—
81C2×C32—42no—
82C2×C32—42no—
83C2×C32C22×D312yes—
84C2×C32C22×D311yescharacteristic
85C3⋊D3—21no—
86C3⋊D3—22no—
87C3⋊D3#6712yescomplemented
88C3×D3—34no—
89C3×D3—62no—
90C3×D3—62no—
91C3×D3—62no—
92C3×D3—62no—
93C3×D3—62no—
94C3×D3—122no—
95C2×D4—271noSylow
96C22×C3—21no—
97C22×C3—22no—
98C22×C3—41no—
99C22×C3—91no—
100C22×C3—91no—
101C22×C3—92no—
102C22×C3—182no—
103C22×C3D3211yescharacteristic, complemented
104C22×C3D3212yescomplemented
105C2×D3—32no—
106C2×D3—32no—
107C2×D3—32no—
108C2×D3—32no—
109C2×D3—61no—
110C2×D3—61no—
111C2×D3—62no—
112C2×D3—64no—
113C2×D3—64no—
114C2×D3—184no—
115C2×D3—182no—
116C3×C4—92no—
117Dic3—32no—
118Dic3—32no—
119Dic3—62no—
120C32—22no—
121C32—21no—
122C32—41no—
123C32D3×D412yescomplemented
124C32C2×#6711yescharacteristic, complemented
125C23—91no—
126C23—271no—
127D4—92no—
128D4—272no—
129C2×C4—271no—
130C2×C3—22no—
131C2×C3—22no—
132C2×C3—21no—
133C2×C3—22no—
134C2×C3—21no—
135C2×C3—42no—
136C2×C3—42no—
137C2×C3—41no—
138C2×C3—92no—
139C2×C3—182no—
140C2×C3—181no—
141C2×C3C2×D3212yes—
142C2×C3C2×D3211yescharacteristic
143D3—34no—
144D3—62no—
145D3—62no—
146D3—62no—
147D3—62no—
148D3—62no—
149D3—122no—
150C22—91no—
151C22—92no—
152C22—91no—
153C22—182no—
154C22—542no—
155C22#111311yescharacteristic, complemented
156C4—92no—
157C3—21no—
158C3—22no—
159C3—41no—
160C3D3×#6712yescomplemented
161C3#381111yescharacteristic, complemented
162C2—21no—
163C2—92no—
164C2—181no—
165C2—182no—
166C2C2×#111311yescharacteristic
subgroupG/H
center, FrattiniC2C2×#1113
commutator, socle, cosocleC2×C33C23
FittingC22×C33C22
hypercenterC22#1113
hypocenterC33C2×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C3×C3⋊D3C2semidirect
2. C2×#1113C2semidirect
3. C3×#638C2semidirect
4. #6295C2semidirect
5. #6294C2semidirect
8. C22×C33C22semidirect
11. C2×C3×C3⋊D3C22semidirect
12. C2×C3×C3⋊D3C22semidirect
14. C3×C3⋊Dic3C22semidirect
15. C22×C3⋊D3D3semidirect
20. #638D3semidirect
33. C3×C3⋊D3D4semidirect
39. C22×C32C2×D3semidirect
40. C22×C32C2×D3semidirect
43. C2×C3⋊D3C2×D3semidirect
44. C2×C3⋊D3C2×D3semidirect
56. C3⋊Dic3C2×D3semidirect
60. C33C2×D4semidirect
87. C3⋊D3#67semidirect
103. C22×C3D32semidirect
104. C22×C3D32semidirect
123. C32D3×D4semidirect
124. C32C2×#67semidirect
155. C22#1113semidirect
160. C3D3×#67semidirect
161. C3#3811semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C3⋊D32
C2×#11132
C3×#6382
#62952
#62942
#38113
D3×#673