Finite Group Databasebeta

← C22×C3×D3×C27 #14518474

Subgroups — C22×C3×D3×C27 #14518474

Order 1944.

558 conjugacy classes of subgroups; only the 294 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 294 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×C32×C27C211yesmaximal, characteristic, complemented
2C2×C3×D3×C27C216yesmaximal, direct product factor
3C22×C3×D3×C9C311yesmaximal, characteristic
4C23×C3×C27—31nomaximal
5C22×D3×C27C313yesmaximal, direct product factor
6C2×C32×C27C2213yescomplemented
7C3×D3×C27C2214yesdirect product factor
8C22×C32×C9C2×C311yescharacteristic
9C2×C3×D3×C9C2×C316yes—
10C22×C3×C27—21no—
11C22×C3×C27—23no—
12C22×C3×C27—36no—
13C22×C3×C27D311yescharacteristic, direct product factor
14C22×C3×C27C2×C313yescomplemented
15C2×D3×C27C2×C3118yesdirect product factor
16C32×C27C2311yescharacteristic, complemented, Sylow
17C22×C32×D3C911yescharacteristic
18C23×C3×C9—31no—
19C22×D3×C9C912yes—
20C22×D3×C9C3211yescharacteristic
21C23×C27—33no—
22C2×C32×C9C22×C313yes—
23C3×D3×C9C22×C314yes—
24C2×C3×C27—23no—
25C2×C3×C27—29no—
26C2×C3×C27—34no—
27C2×C3×C27C2×D313yesdirect product factor
28C2×C3×C27C22×C319yescomplemented
29D3×C27C22×C3112yesdirect product factor
30C22×C33C2×C911yescharacteristic
31C2×C32×D3C2×C916yes—
32C22×C3×C9—21no—
33C22×C3×C9—22no—
34C22×C3×C9—21no—
35C22×C3×C9—36no—
36C22×C3×C9C2×C912yes—
37C22×C3×C9C3×D311yescharacteristic
38C22×C3×C9C2×C3211yescharacteristic
39C2×D3×C9C2×C9112yes—
40C2×D3×C9C2×C3216yes—
41C22×C27—23no—
42C22×C27—318no—
43C22×C27C3×D313yesdirect product factor
44C32×C9C23×C311yescharacteristic
45C3×C27—21no—
46C3×C27—23no—
47C3×C27C22×D311yescharacteristic, direct product factor
48C3×C27C23×C313yescomplemented
49C23×C32—31no—
50C22×C3×D3C2713yesdirect product factor
51C22×C3×D3C3×C911yescharacteristic
52C23×C9—32no—
53C23×C9—31no—
54C2×C33C22×C913yes—
55C32×D3C22×C914yes—
56C2×C3×C9—23no—
57C2×C3×C9—26no—
58C2×C3×C9—23no—
59C2×C3×C9—34no—
60C2×C3×C9C22×C916yes—
61C2×C3×C9C2×C3×D313yes—
62C2×C3×C9C22×C3213yes—
63D3×C9C22×C918yes—
64D3×C9C22×C3214yes—
65C2×C27—29no—
66C2×C27—312no—
67C2×C27C2×C3×D319yesdirect product factor
68C22×C32—23no—
69C22×C32—21no—
70C22×C32—36no—
71C22×C32C2×C2713yescomplemented
72C22×C32D3×C911yescharacteristic
73C22×C32C2×C3×C911yescharacteristic
74C2×C3×D3C2×C27118yesdirect product factor
75C2×C3×D3C2×C3×C916yes—
76C22×C9—22no—
77C22×C9—21no—
78C22×C9—312no—
79C22×C9—36no—
80C22×C9D3×C912yes—
81C22×C9C32×D311yescharacteristic
82C33C23×C911yescharacteristic
83C3×C9—21no—
84C3×C9—22no—
85C3×C9—21no—
86C3×C9C23×C912yes—
87C3×C9C22×C3×D311yescharacteristic
88C3×C9C23×C3211yescharacteristic
89C27—23no—
90C27C22×C3×D313yesdirect product factor
91C23×C3—33no—
92C23×C3—31no—
93C22×D3C3×C2711yescharacteristic, direct product factor
94C2×C32—29no—
95C2×C32—23no—
96C2×C32—34no—
97C2×C32C22×C2719yescomplemented
98C2×C32C2×D3×C913yes—
99C2×C32C22×C3×C913yes—
100C3×D3C22×C27112yesdirect product factor
101C3×D3C22×C3×C914yes—
102C2×C9—26no—
103C2×C9—23no—
104C2×C9—38no—
105C2×C9—34no—
106C2×C9C2×D3×C916yes—
107C2×C9C2×C32×D313yes—
108C22×C3—23no—
109C22×C3—21no—
110C22×C3—318no—
111C22×C3—36no—
112C22×C3D3×C2713yesdirect product factor
113C22×C3C2×C3×C2711yescharacteristic, complemented
114C22×C3C3×D3×C911yescharacteristic
115C2×D3C2×C3×C2716yesdirect product factor
116C32—23no—
117C32—21no—
118C32C23×C2713yescomplemented
119C32C22×D3×C911yescharacteristic
120C32C23×C3×C911yescharacteristic
121C9—22no—
122C9—21no—
123C9C22×D3×C912yes—
124C9C22×C32×D311yescharacteristic
125C23—31noSylow
126C2×C3—29no—
127C2×C3—23no—
128C2×C3—312no—
129C2×C3—34no—
130C2×C3C2×D3×C2719yesdirect product factor
131C2×C3C22×C3×C2713yescomplemented
132C2×C3C2×C3×D3×C913yes—
133D3C22×C3×C2714yesdirect product factor
134C22—36no—
135C22C3×D3×C2711yescharacteristic, direct product factor
136C3—23no—
137C3—21no—
138C3C22×D3×C2713yesdirect product factor
139C3C23×C3×C2711yescharacteristic, complemented
140C3C22×C3×D3×C911yescharacteristic
141C2—34no—
142C2C2×C3×D3×C2713yesdirect product factor
subgroupG/H
center, hypercenterC22×C3×C27D3
commutator, hypocenterC3C23×C3×C27
FrattiniC9C22×C32×D3
FittingC22×C32×C27C2
socleC22×C33C2×C9
prime radicalC22×C32×D3C9
cosocleC3×C9C23×C32
LCSG ▷ C3
UCSC1 ◁ C22×C3×C27

Complements

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

NH ≅ G/Ntype
1. C22×C32×C27C2semidirect
2. C2×C3×D3×C27C2direct (N × H)
5. C22×D3×C27C3direct (N × H)
6. C2×C32×C27C22semidirect
7. C3×D3×C27C22direct (N × H)
13. C22×C3×C27D3direct (N × H)
14. C22×C3×C27C2×C3semidirect
15. C2×D3×C27C2×C3direct (N × H)
16. C32×C27C23semidirect
27. C2×C3×C27C2×D3direct (N × H)
28. C2×C3×C27C22×C3semidirect
29. D3×C27C22×C3direct (N × H)
43. C22×C27C3×D3direct (N × H)
47. C3×C27C22×D3direct (N × H)
48. C3×C27C23×C3semidirect
50. C22×C3×D3C27direct (N × H)
67. C2×C27C2×C3×D3direct (N × H)
71. C22×C32C2×C27semidirect
74. C2×C3×D3C2×C27direct (N × H)
90. C27C22×C3×D3direct (N × H)
93. C22×D3C3×C27direct (N × H)
97. C2×C32C22×C27semidirect
100. C3×D3C22×C27direct (N × H)
112. C22×C3D3×C27direct (N × H)
113. C22×C3C2×C3×C27semidirect
115. C2×D3C2×C3×C27direct (N × H)
118. C32C23×C27semidirect
130. C2×C3C2×D3×C27direct (N × H)
131. C2×C3C22×C3×C27semidirect
133. D3C22×C3×C27direct (N × H)
135. C22C3×D3×C27direct (N × H)
138. C3C22×D3×C27direct (N × H)
139. C3C23×C3×C27semidirect
142. C2C2×C3×D3×C27direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×C272
C2×C3×D3×C272
C22×C3×D3×C93
C23×C3×C273
C22×D3×C273