Finite Group Databasebeta

← C3×C42×C22⋊C9 #13152159

Subgroups — C3×C42×C22⋊C9 #13152159

Order 1728.

738 conjugacy classes of subgroups; only the 240 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 240 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×C3×C4×C22⋊C9C213yesmaximal
2C22×C32×C42C311yesmaximal, characteristic
3C42×C22⋊C9C313yesmaximal, direct product factor
4C22×C3×C22⋊C9C2211yescharacteristic
5C3×C4×C22⋊C9C416yesdirect product factor
6C3×C42×C9—41nomaximal
7C23×C32×C4C2×C313yes—
8C2×C32×C42—31no—
9C2×C32×C42—33no—
10C2×C4×C22⋊C9C2×C319yes—
11C2×C3×C22⋊C9C2×C413yes—
12C2×C3×C4×C9—43no—
13C22×C3×C42C913yescomplemented
14C22×C3×C42C3211yescharacteristic
15C24×C32C22×C311yescharacteristic
16C22×C32×C4—33no—
17C22×C32×C4—36no—
18C22×C32×C4—33no—
19C22×C32×C4C3×C416yes—
20C22×C22⋊C9C22×C313yes—
21C32×C42—32no—
22C32×C42—33no—
23C32×C42A411yescharacteristic
24C4×C22⋊C9C3×C4118yesdirect product factor
25C42×C9—43no—
26C22×C3×C9—41no—
27C3×C22⋊C9C4211yescharacteristic, direct product factor
28C3×C4×C9—46no—
29C23×C3×C4C2×C919yes—
30C23×C3×C4C2×C3213yes—
31C2×C3×C42—33no—
32C2×C3×C42—31no—
33C2×C3×C42—39no—
34C2×C3×C42—33no—
35C23×C32—33no—
36C23×C32—31no—
37C23×C32C2×C3×C413yes—
38C2×C32×C4—36no—
39C2×C32×C4—33no—
40C2×C32×C4—36no—
41C2×C32×C4—36no—
42C2×C32×C4—36no—
43C2×C32×C4C2×A413yes—
44C2×C22⋊C9C2×C3×C419yes—
45C2×C4×C9—49no—
46C22×C42C3×C911yescharacteristic, complemented, Sylow
47C2×C3×C9—43no—
48C24×C3C22×C913yes—
49C24×C3C22×C3211yescharacteristic
50C22×C3×C4—39no—
51C22×C3×C4—33no—
52C22×C3×C4—39no—
53C22×C3×C4—33no—
54C22×C3×C4—318no—
55C22×C3×C4—36no—
56C22×C3×C4C4×C9118yescomplemented
57C22×C3×C4C32×C416yes—
58C3×C42—32no—
59C3×C42—36no—
60C3×C42—39no—
61C3×C42—33no—
62C3×C42C22⋊C913yesdirect product factor
63C3×C42C3×A411yescharacteristic
64C22×C32—33no—
65C22×C32—32no—
66C22×C32—33no—
67C22×C32—33no—
68C22×C32C3×C4211yescharacteristic
69C22×C32C22×A411yescharacteristic
70C32×C4—36no—
71C32×C4C4×A416yes—
72C22×C9—43no—
73C22⋊C9C3×C4213yesdirect product factor
74C4×C9—418no—
75C23×C4C2×C3×C913yes—
76C2×C42—31no—
77C2×C42—33no—
78C3×C9—41noSylow
79C23×C3—39no—
80C23×C3—33no—
81C23×C3—31no—
82C23×C3—33no—
83C23×C3C2×C4×C919yes—
84C23×C3C2×C32×C413yes—
85C2×C3×C4—36no—
86C2×C3×C4—318no—
87C2×C3×C4—33no—
88C2×C3×C4—39no—
89C2×C3×C4—318no—
90C2×C3×C4—318no—
91C2×C3×C4—36no—
92C2×C3×C4—36no—
93C2×C3×C4—318no—
94C2×C3×C4—36no—
95C2×C3×C4C2×C22⋊C919yes—
96C2×C3×C4C2×C3×A413yes—
97C2×C32—33no—
98C2×C32—31no—
99C2×C32C2×C4×A413yes—
100C2×C9—49no—
101C24C22×C3×C911yescharacteristic
102C22×C4—33no—
103C22×C4—33no—
104C22×C4—36no—
105C22×C4C3×C4×C916yescomplemented
106C42—32no—
107C42—33no—
108C42C3×C22⋊C911yescharacteristic, direct product factor
109C22×C3—39no—
110C22×C3—33no—
111C22×C3—36no—
112C22×C3—32no—
113C22×C3—33no—
114C22×C3—33no—
115C22×C3—39no—
116C22×C3—39no—
117C22×C3C42×C913yescomplemented
118C22×C3C32×C4211yescharacteristic
119C22×C3C22×C22⋊C913yes—
120C22×C3C22×C3×A411yescharacteristic
121C3×C4—36no—
122C3×C4—318no—
123C3×C4C4×C22⋊C9118yesdirect product factor
124C3×C4C3×C4×A416yes—
125C32C42×A411yescharacteristic
126C9—43no—
127C23—33no—
128C23—31no—
129C23C2×C3×C4×C913yes—
130C2×C4—36no—
131C2×C4—33no—
132C2×C4—36no—
133C2×C4—36no—
134C2×C4—36no—
135C2×C4C2×C3×C22⋊C913yes—
136C2×C3—33no—
137C2×C3—39no—
138C2×C3—31no—
139C2×C3—33no—
140C2×C3C2×C4×C22⋊C919yes—
141C2×C3C2×C3×C4×A413yes—
142C22—33no—
143C22—32no—
144C22—33no—
145C22—33no—
146C22C3×C42×C911yescharacteristic, complemented
147C22C22×C3×C22⋊C911yescharacteristic
148C4—36no—
149C4C3×C4×C22⋊C916yesdirect product factor
150C3C42×C22⋊C913yesdirect product factor
151C3C3×C42×A411yescharacteristic
152C2—31no—
153C2—33no—
154C2C2×C3×C4×C22⋊C913yes—
subgroupG/H
center, hypercenterC32×C42A4
commutator, hypocenterC22C3×C42×C9
FrattiniC22×C3C22×C3×A4
FittingC22×C32×C42C3
socle, prime radicalC24×C32C22×C3
cosocleC24×C3C22×C32
LCSG ▷ C22
UCSC1 ◁ C32×C42

Complements

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

NH ≅ G/Ntype
3. C42×C22⋊C9C3direct (N × H)
5. C3×C4×C22⋊C9C4direct (N × H)
13. C22×C3×C42C9semidirect
24. C4×C22⋊C9C3×C4direct (N × H)
27. C3×C22⋊C9C42direct (N × H)
46. C22×C42C3×C9semidirect
56. C22×C3×C4C4×C9semidirect
62. C3×C42C22⋊C9direct (N × H)
73. C22⋊C9C3×C42direct (N × H)
105. C22×C4C3×C4×C9semidirect
108. C42C3×C22⋊C9direct (N × H)
117. C22×C3C42×C9semidirect
123. C3×C4C4×C22⋊C9direct (N × H)
146. C22C3×C42×C9semidirect
149. C4C3×C4×C22⋊C9direct (N × H)
150. C3C42×C22⋊C9direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×C22⋊C92
C22×C32×C423
C42×C22⋊C93
C3×C42×C94