Finite Group Databasebeta

← C4×#88813 #13161832

Subgroups — C4×#88813 #13161832

Order 1728.

1410 conjugacy classes of subgroups; only the 399 normal subgroups are shown.

normal subgroups only

This group has 1410 conjugacy classes of subgroups — too many to draw. Only its 399 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×C3⋊Dic3C213yesmaximal
2C2×#88813C214yesmaximal
3C4×Dic32—33nomaximal
4C22×C33×C4C2211yescharacteristic
5C22×C3×C3⋊Dic3C2216yes—
6C3×C4×C3⋊Dic3C4112yescomplemented
7#88813C4116yesdirect product factor
8C2×C4×C3⋊Dic3D313yes—
9C2×C3×C4×Dic3—36no—
10C2×C3×C4×Dic3—63no—
11C2×Dic32—312no—
12C23×C33C2311yescharacteristic
13C2×C33×C4C2×C416yes—
14C2×C3×C3⋊Dic3C2×C4124yes—
15C2×C3×C3⋊Dic3C2×C4112yes—
16C42×Dic3—93no—
17C22×C32×C4—23no—
18C22×C32×C4—41no—
19C22×C32×C4C2×D313yes—
20C22×C3⋊Dic3C2×D316yes—
21C22×C3×Dic3—312no—
22C22×C3×Dic3—66no—
23C4×C3⋊Dic3Dic3112yescomplemented
24C3×C4×Dic3—324no—
25C3×C4×Dic3—612no—
26Dic32—348no—
27C22×C33C22×C414yes—
28C22×C33C22×C413yes—
29C33×C4C4214yescomplemented
30C3×C3⋊Dic3C42124yescomplemented
31C2×C3×C42—93no—
32C2×C4×Dic3—36no—
33C2×C4×Dic3—63no—
34C2×C4×Dic3—912no—
35C23×C32—23no—
36C23×C32—41no—
37C23×C32C22×D313yes—
38C2×C32×C4—212no—
39C2×C32×C4—26no—
40C2×C32×C4—46no—
41C2×C32×C4C4×D3112yes—
42C2×C32×C4C2×Dic316yes—
43C2×C3⋊Dic3C4×D3124yes—
44C2×C3⋊Dic3C2×Dic3112yes—
45C2×C3×Dic3—348no—
46C2×C3×Dic3—324no—
47C2×C3×Dic3—612no—
48C2×C3×Dic3—624no—
49C43—271noSylow
50C2×C33C2×C4216yes—
51C2×C33C2×C4211yescharacteristic
52C22×C3×C4—23no—
53C22×C3×C4—41no—
54C22×C3×C4—96no—
55C22×C3×C4D3213yes—
56C22×Dic3—312no—
57C22×Dic3—66no—
58C3×C42—912no—
59C4×Dic3—324no—
60C4×Dic3—612no—
61C4×Dic3—948no—
62C22×C32—212no—
63C22×C32—26no—
64C22×C32—23no—
65C22×C32—43no—
66C22×C32—44no—
67C22×C32C2×C4×D3112yes—
68C22×C32C2×C4×D316yes—
69C22×C32C22×Dic313yes—
70C32×C4—212no—
71C32×C4—44no—
72C32×C4C4×Dic3112yescomplemented
73C3⋊Dic3C4×Dic3124yescomplemented
74C3×Dic3—348no—
75C3×Dic3—624no—
76C2×C42—93no—
77C2×C42—274no—
78C33C4311yescharacteristic, complemented, Sylow
79C23×C3—23no—
80C23×C3—41no—
81C23×C3C2×D3213yes—
82C2×C3×C4—212no—
83C2×C3×C4—26no—
84C2×C3×C4—46no—
85C2×C3×C4—924no—
86C2×C3×C4—912no—
87C2×C3×C4D3×Dic3112yes—
88C2×C3×C4#62416yes—
89C2×Dic3—348no—
90C2×Dic3—324no—
91C2×Dic3—624no—
92C2×Dic3—612no—
93C2×C32—212no—
94C2×C32—26no—
95C2×C32—23no—
96C2×C32—41no—
97C2×C32—46no—
98C2×C32C42×D3112yes—
99C2×C32C2×C4×Dic316yes—
100C2×C32C2×C4×Dic313yes—
101C22×C4—96no—
102C22×C4#111311yescharacteristic
103C42—912no—
104C42—2716no—
105C22×C3—212no—
106C22×C3—23no—
107C22×C3—26no—
108C22×C3—44no—
109C22×C3—43no—
110C22×C3C4×D32112yes—
111C22×C3C2×D3×Dic316yes—
112C22×C3C2×#62413yes—
113C3×C4—212no—
114C3×C4—44no—
115C3×C4—924no—
116C3×C4Dic32112yescomplemented
117Dic3—348no—
118Dic3—624no—
119C32—23no—
120C32—41no—
121C32C42×Dic313yescomplemented
122C23C2×#111311yescharacteristic
123C2×C4—924no—
124C2×C4—912no—
125C2×C4#629416yes—
126C2×C3—26no—
127C2×C3—212no—
128C2×C3—23no—
129C2×C3—46no—
130C2×C3—41no—
131C2×C3C4×D3×Dic3112yes—
132C2×C3C4×#62416yes—
133C2×C3C2×Dic3213yes—
134C22C4×#111314yes—
135C22C2×#629413yes—
136C4—924no—
137C4#8881314yesdirect product factor
138C3—23no—
139C3—41no—
140C3C4×Dic3213yescomplemented
141C2C4×#629416yes—
142C2C2×#8881311yescharacteristic
subgroupG/H
center, hypercenterC22×C4#1113
commutator, hypocenterC33C43
FrattiniC23C2×#1113
FittingC22×C33×C4C22
socle, prime radical, cosocleC23×C33C23
LCSG ▷ C33
UCSC1 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
6. C3×C4×C3⋊Dic3C4semidirect
7. #88813C4direct (N × H)
23. C4×C3⋊Dic3Dic3semidirect
29. C33×C4C42semidirect
30. C3×C3⋊Dic3C42semidirect
72. C32×C4C4×Dic3semidirect
73. C3⋊Dic3C4×Dic3semidirect
78. C33C43semidirect
116. C3×C4Dic32semidirect
121. C32C42×Dic3semidirect
137. C4#88813direct (N × H)
140. C3C4×Dic32semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×C3⋊Dic32
C2×#888132
C4×Dic323