Finite Group Databasebeta

← C3×#3811 #89012

Subgroups — C3×#3811 #89012

Order 432.

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

normal subgroups only

This group has 290 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
1C22×C3×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3×D32C211yesmaximal, characteristic, complemented
3C32×#67C212yesmaximal, complemented
4C3×#626C212yesmaximal, complemented
5C3×#624C211yesmaximal, characteristic, complemented
6C3×D3×D4—32nomaximal
7#3811C311yesmaximal, characteristic, direct product factor
8C22×C33C2211yescharacteristic, complemented
9C2×C3×C3⋊D3—22no—
10C2×C3×C3⋊D3C2211yescharacteristic
11C2×C3×C3⋊D3C2211yescharacteristic, complemented
12C2×C32×D3C2212yescomplemented
13C3×D32—22no—
14C32×Dic3C2212yescomplemented
15C22×C3⋊D3C2×C311yescharacteristic, complemented
16C22×C3×D3—32no—
17C22×C3×D3—32no—
18C22×C3×D3—61no—
19C2×D32C2×C311yescharacteristic, complemented
20C32×D4—32no—
21C3×#67—22no—
22C3×#67—32no—
23C3×#67D312yescomplemented
24C3×#67C2×C312yescomplemented
25C3×D12—32no—
26C3×C4×D3—32no—
27#626C2×C312yescomplemented
28#624C2×C311yescharacteristic, complemented
29C2×C33—21no—
30C2×C33C2311yescharacteristic
31C3×C3⋊D3—21no—
32C3×C3⋊D3D412yescomplemented
33C32×D3—22no—
34C2×C3×D4—91no—
35D3×D4—32no—
36C22×C32—21no—
37C22×C32—22no—
38C22×C32—32no—
39C22×C32—41no—
40C22×C32C2×D312yescomplemented
41C22×C32C22×C311yescharacteristic, complemented
42C2×C3⋊D3—22no—
43C2×C3⋊D3C22×C311yescharacteristic
44C2×C3⋊D3C22×C311yescharacteristic, complemented
45C2×C3×D3—22no—
46C2×C3×D3—32no—
47C2×C3×D3—32no—
48C2×C3×D3—61no—
49C2×C3×D3—61no—
50C2×C3×D3—64no—
51C2×C3×D3—64no—
52C2×C3×D3—64no—
53C2×C3×D3C2×D312yescomplemented
54C2×C3×D3C22×C312yescomplemented
55D32—22no—
56C32×C4—32no—
57C3×Dic3—22no—
58C3×Dic3C2×D312yescomplemented
59C3×Dic3C22×C312yescomplemented
60C33C2×D411yescharacteristic, complemented, Sylow
61C23×C3—91no—
62C23×C3—91no—
63C22×D3—32no—
64C22×D3—32no—
65C22×D3—61no—
66C3×D4—32no—
67C3×D4—32no—
68C3×D4—62no—
69C3×D4—92no—
70C2×C3×C4—91no—
71#67—32no—
72#67C3×D312yescomplemented
73D12—32no—
74C4×D3—32no—
75C2×C32—21no—
76C2×C32—22no—
77C2×C32—22no—
78C2×C32—21no—
79C2×C32—22no—
80C2×C32—41no—
81C2×C32—42no—
82C2×C32—42no—
83C2×C32—62no—
84C2×C32C22×D312yes—
85C2×C32C23×C311yescharacteristic
86C3⋊D3—21no—
87C3⋊D3C3×D412yescomplemented
88C3×D3—22no—
89C3×D3—22no—
90C3×D3—34no—
91C3×D3—42no—
92C3×D3—62no—
93C3×D3—62no—
94C3×D3—62no—
95C2×D4—91noSylow
96C22×C3—21no—
97C22×C3—22no—
98C22×C3—32no—
99C22×C3—32no—
100C22×C3—41no—
101C22×C3—62no—
102C22×C3—91no—
103C22×C3—91no—
104C22×C3—182no—
105C22×C3—182no—
106C22×C3D3211yescharacteristic, complemented
107C22×C3C2×C3×D312yescomplemented
108C2×D3—32no—
109C2×D3—32no—
110C2×D3—61no—
111C2×D3—61no—
112C2×D3—64no—
113C2×D3—64no—
114C2×D3—64no—
115C2×D3C2×C3×D312yescomplemented
116C3×C4—32no—
117C3×C4—32no—
118C3×C4—62no—
119Dic3C2×C3×D312yescomplemented
120C32—21no—
121C32—22no—
122C32—41no—
123C32D3×D412yescomplemented
124C32C2×C3×D411yescharacteristic, complemented
125C23—91no—
126C23—91no—
127D4—32no—
128D4—92no—
129C2×C4—91no—
130C2×C3—22no—
131C2×C3—21no—
132C2×C3—22no—
133C2×C3—22no—
134C2×C3—21no—
135C2×C3—42no—
136C2×C3—42no—
137C2×C3—41no—
138C2×C3—62no—
139C2×C3—62no—
140C2×C3—92no—
141C2×C3—122no—
142C2×C3—181no—
143C2×C3C2×D3211yescharacteristic
144C2×C3C22×C3×D312yes—
145D3—22no—
146D3—34no—
147D3—62no—
148D3—62no—
149D3—62no—
150C22—32no—
151C22—91no—
152C22—91no—
153C22—182no—
154C22—182no—
155C22C3×D3211yescharacteristic, complemented
156C4—32no—
157C3—21no—
158C3—22no—
159C3—41no—
160C3#381111yescharacteristic, direct product factor
161C3C3×D3×D412yescomplemented
162C2—21no—
163C2—62no—
164C2—92no—
165C2—181no—
166C2C2×C3×D3211yescharacteristic
subgroupG/H
centerC2×C3C2×D32
commutator, cosocleC2×C32C23×C3
FrattiniC2C2×C3×D32
FittingC22×C33C22
socleC2×C33C23
hypercenterC22×C3D32
hypocenterC32C2×C3×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C22×C3×C3⋊D3C2semidirect
2. C2×C3×D32C2semidirect
3. C32×#67C2semidirect
4. C3×#626C2semidirect
5. C3×#624C2semidirect
7. #3811C3direct (N × H)
8. C22×C33C22semidirect
11. C2×C3×C3⋊D3C22semidirect
12. C2×C32×D3C22semidirect
14. C32×Dic3C22semidirect
15. C22×C3⋊D3C2×C3semidirect
19. C2×D32C2×C3semidirect
23. C3×#67D3semidirect
24. C3×#67C2×C3semidirect
27. #626C2×C3semidirect
28. #624C2×C3semidirect
32. C3×C3⋊D3D4semidirect
40. C22×C32C2×D3semidirect
41. C22×C32C22×C3semidirect
44. C2×C3⋊D3C22×C3semidirect
53. C2×C3×D3C2×D3semidirect
54. C2×C3×D3C22×C3semidirect
58. C3×Dic3C2×D3semidirect
59. C3×Dic3C22×C3semidirect
60. C33C2×D4semidirect
72. #67C3×D3semidirect
87. C3⋊D3C3×D4semidirect
106. C22×C3D32semidirect
107. C22×C3C2×C3×D3semidirect
115. C2×D3C2×C3×D3semidirect
119. Dic3C2×C3×D3semidirect
123. C32D3×D4semidirect
124. C32C2×C3×D4semidirect
155. C22C3×D32semidirect
160. C3#3811direct (N × H)
161. C3C3×D3×D4semidirect

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×C3×D322
C32×#672
C3×#6262
C3×#6242
C3×D3×D43
#38113