Finite Group Databasebeta

← #88668

Subgroups — #88668

Order 432.

194 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 43 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⋊D9C211yesmaximal, characteristic, complemented
2C2×D3×D9C211yesmaximal, characteristic, complemented
3C9×#67C211yesmaximal, characteristic, complemented
4C3×#611C211yesmaximal, characteristic, complemented
5#6195C211yesmaximal, characteristic, complemented
6#6192C211yesmaximal, characteristic, complemented
7(C3⋊D9)⋊C4C211yesmaximal, characteristic, complemented
8#3811—31nomaximal
9D4×D9—31nomaximal
10C22×C3×C9C2211yescharacteristic, complemented
11C2×C3⋊D9—22no—
12C2×C3⋊D9C2211yescharacteristic
13C2×C3⋊D9C2211yescharacteristic, complemented
14C2×D3×C9C2211yescharacteristic, complemented
15C2×C3×D9C2211yescharacteristic, complemented
16D3×D9—22no—
17C9×Dic3C2211yescharacteristic, complemented
18C3×Dic9C2211yescharacteristic, complemented
19C22×C3⋊D3—31no—
20C2×D32—31no—
21C3×#67—31no—
22C3×#67D311yescharacteristic
23#626—31no—
24#626—31no—
25#624—31no—
26C22×D9—31no—
27C22×D9—31no—
28C22×D9—61no—
29D4×C9—31no—
30#611—31no—
31#611D311yescharacteristic, complemented
32D36—31no—
33C4×D9—31no—
34C2×C3×C9—21no—
35C2×C3×C9C2311yescharacteristic
36C3⋊D9—21no—
37C3⋊D9D412yescomplemented
38D3×C9—21no—
39C3×D9—21no—
40D3×D4—91no—
41D3×D4—91no—
42C22×C32C2×D311yescharacteristic
43C2×C3⋊D3—31no—
44C2×C3⋊D3—31no—
45C2×C3⋊D3—62no—
46C2×C3×D3—31no—
47C2×C3×D3C2×D311yescharacteristic
48D32—62no—
49C3×Dic3—31no—
50C3×Dic3C2×D311yescharacteristic
51C22×C9—21no—
52C22×C9—31no—
53C22×C9C2×D311yescharacteristic, complemented
54C2×D9—31no—
55C2×D9—31no—
56C2×D9—61no—
57C2×D9—61no—
58C2×D9—62no—
59C2×D9—62no—
60C2×D9—64no—
61C2×D9C2×D311yescharacteristic, complemented
62C4×C9—31no—
63Dic9C2×D311yescharacteristic, complemented
64C3×C9C2×D411yescharacteristic, complemented, Sylow
65C22×D3—91no—
66C22×D3—91no—
67C22×D3—91no—
68C22×D3—91no—
69C22×D3—181no—
70C3×D4—31no—
71C3×D4—91no—
72#67—31no—
73#67—91no—
74#67—91no—
75#67D911yescharacteristic, complemented
76D12—91no—
77D12—91no—
78C4×D3—91no—
79C4×D3—91no—
80C2×C32—21no—
81C2×C32C22×D311yescharacteristic
82C3⋊D3—32no—
83C3⋊D3—61no—
84C3×D3—21no—
85C3×D3—61no—
86C2×C9—22no—
87C2×C9—21no—
88C2×C9—21no—
89C2×C9—61no—
90C2×C9C22×D311yescharacteristic
91D9—21no—
92D9—32no—
93D9—62no—
94D9—62no—
95D9—61no—
96C2×D4—271noSylow
97C22×C3—21no—
98C22×C3—31no—
99C22×C3—91no—
100C22×C3C2×D911yescharacteristic, complemented
101C22×C3D3211yescharacteristic
102C2×D3—31no—
103C2×D3—91no—
104C2×D3—91no—
105C2×D3—91no—
106C2×D3—91no—
107C2×D3—181no—
108C2×D3—181no—
109C2×D3—182no—
110C2×D3—182no—
111C2×D3—182no—
112C2×D3—182no—
113C2×D3—184no—
114C2×D3C2×D911yescharacteristic, complemented
115C3×C4—31no—
116C3×C4—91no—
117Dic3—31no—
118Dic3C2×D911yescharacteristic, complemented
119C32D3×D411yescharacteristic
120C9—21no—
121C9D3×D411yescharacteristic, complemented
122C23—271no—
123C23—271no—
124D4—31no—
125D4—91no—
126D4—271no—
127D4—271no—
128C2×C4—271no—
129C2×C3—22no—
130C2×C3—21no—
131C2×C3—21no—
132C2×C3—21no—
133C2×C3—61no—
134C2×C3—181no—
135C2×C3C22×D911yescharacteristic
136C2×C3C2×D3211yescharacteristic
137D3—21no—
138D3—61no—
139D3—92no—
140D3—92no—
141D3—182no—
142D3—182no—
143D3—181no—
144D3—181no—
145C22—31no—
146C22—91no—
147C22—271no—
148C22—271no—
149C22—542no—
150C22—542no—
151C22D3×D911yescharacteristic, complemented
152C4—31no—
153C4—91no—
154C3—21no—
155C3D4×D911yescharacteristic, complemented
156C3#381111yescharacteristic
157C2—21no—
158C2—61no—
159C2—181no—
160C2—272no—
161C2—541no—
162C2C2×D3×D911yescharacteristic
subgroupG/H
centerC2C2×D3×D9
commutator, cosocleC2×C3×C9C23
FrattiniC2×C3C2×D32
FittingC22×C3×C9C22
socleC2×C32C22×D3
hypercenterC22D3×D9
hypocenterC3×C9C2×D4
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C3⋊D9C2semidirect
2. C2×D3×D9C2semidirect
3. C9×#67C2semidirect
4. C3×#611C2semidirect
5. #6195C2semidirect
6. #6192C2semidirect
7. (C3⋊D9)⋊C4C2semidirect
10. C22×C3×C9C22semidirect
13. C2×C3⋊D9C22semidirect
14. C2×D3×C9C22semidirect
15. C2×C3×D9C22semidirect
17. C9×Dic3C22semidirect
18. C3×Dic9C22semidirect
31. #611D3semidirect
37. C3⋊D9D4semidirect
53. C22×C9C2×D3semidirect
61. C2×D9C2×D3semidirect
63. Dic9C2×D3semidirect
64. C3×C9C2×D4semidirect
75. #67D9semidirect
100. C22×C3C2×D9semidirect
114. C2×D3C2×D9semidirect
118. Dic3C2×D9semidirect
121. C9D3×D4semidirect
151. C22D3×D9semidirect
155. C3D4×D9semidirect

Maximal subgroups

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

subgroupindex
C22×C3⋊D92
C2×D3×D92
C9×#672
C3×#6112
#61952
#61922
(C3⋊D9)⋊C42
#38113
D4×D93