Finite Group Databasebeta

← C2×D3×Dic21 #11759617

Subgroups — C2×D3×Dic21 #11759617

Order 1008.

232 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 98 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×D3×C7C211yesmaximal, characteristic
2C2×C3⋊Dic21C211yesmaximal, characteristic, complemented
3C2×C3×Dic21C211yesmaximal, characteristic, complemented
4D3×Dic21C214yesmaximal, direct product factor
5C22×Dic21—31nomaximal
6C2×D3×Dic7—31nomaximal
7C22×C32×C7C2211yescharacteristic
8C2×C3×D3×C7C414yescomplemented
9C2×C3×D3×C7C2212yes—
10C3⋊Dic21C2212yescomplemented
11C3×Dic21C2212yescomplemented
12C23×C3×C7—31no—
13C22×D3×C7D311yescharacteristic
14C2×Dic21—31no—
15C2×Dic21—31no—
16C2×Dic21—34no—
17C2×Dic21—61no—
18C2×Dic21D311yescharacteristic, direct product factor
19C2×C3×Dic7—31no—
20D3×Dic7—34no—
21C2×D3×Dic3—71nomaximal, Hall
22C2×C32×C7C2×C412yescomplemented
23C2×C32×C7C2311yescharacteristic
24C3×D3×C7C2×C414yescomplemented
25C22×Dic7—91noHall
26C22×C3×C7—21no—
27C22×C3×C7—34no—
28C22×C3×C7—32no—
29C22×C3×C7C2×D311yescharacteristic
30C22×C3×C7C2×D311yescharacteristic
31C2×D3×C7Dic314yescomplemented
32C2×D3×C7C2×D312yes—
33Dic21—32no—
34Dic21—32no—
35Dic21—62no—
36Dic21C2×D312yesdirect product factor
37C3×Dic7—32no—
38C22×C3×D3D711yescharacteristic
39C2×C3⋊Dic3—71no—
40C2×C3×Dic3—71no—
41D3×Dic3—74no—
42C32×C7C22×C411yescharacteristic, complemented, Hall
43C23×C7—31no—
44C2×Dic7—31no—
45C2×Dic7—94no—
46C2×Dic7—91no—
47C22×Dic3—211no—
48C2×C4×D3—211no—
49C2×C3×C7—22no—
50C2×C3×C7—21no—
51C2×C3×C7—34no—
52C2×C3×C7C4×D312yescomplemented
53C2×C3×C7C2×Dic312yescomplemented
54C2×C3×C7C22×D311yescharacteristic
55C2×C3×C7C22×D311yescharacteristic
56D3×C7C2×Dic314yescomplemented
57C22×C32C2×D711yescharacteristic
58C2×C3×D3Dic714yescomplemented
59C2×C3×D3C2×D712yes—
60C3⋊Dic3—72no—
61C3×Dic3—72no—
62C22×C7—34no—
63C22×C7—32no—
64C22×C7D3211yescharacteristic
65Dic7—32no—
66Dic7—92no—
67C23×C3—31no—
68C22×D3D2111yescharacteristic
69C2×C3×C4—211no—
70C2×Dic3—71no—
71C2×Dic3—214no—
72C2×Dic3—211no—
73C2×Dic3—211no—
74C2×Dic3—421no—
75C4×D3—214no—
76C3×C7—21no—
77C3×C7C2×C4×D311yescharacteristic, complemented
78C3×C7C22×Dic311yescharacteristic, complemented
79C2×C32C2×Dic712yescomplemented
80C2×C32C22×D711yescharacteristic
81C3×D3C2×Dic714yescomplemented
82C22×C4—631noSylow
83C2×C7—34no—
84C2×C7D3×Dic312yescomplemented
85C2×C7C2×D3211yescharacteristic
86C22×C3—21no—
87C22×C3—34no—
88C22×C3—32no—
89C22×C3D3×D711yescharacteristic
90C22×C3C2×D2111yescharacteristic
91C2×D3Dic2114yesdirect product factor
92C2×D3C2×D2112yes—
93C3×C4—212no—
94Dic3—72no—
95Dic3—212no—
96Dic3—212no—
97Dic3—422no—
98C32C22×Dic711yescharacteristic, complemented, Sylow
99C23—31no—
100C2×C4—211no—
101C2×C4—634no—
102C2×C4—631no—
103C7C2×D3×Dic311yescharacteristic, complemented, Sylow
104C2×C3—22no—
105C2×C3—21no—
106C2×C3—34no—
107C2×C3D3×Dic712yescomplemented
108C2×C3C2×Dic2112yescomplemented
109C2×C3C2×D3×D711yescharacteristic
110C2×C3C22×D2111yescharacteristic
111D3C2×Dic2114yesdirect product factor
112C22—34no—
113C22—32no—
114C22D3×D2111yescharacteristic
115C4—212no—
116C4—632no—
117C3—21no—
118C3C2×D3×Dic711yescharacteristic, complemented
119C3C22×Dic2111yescharacteristic, complemented
120C2—34no—
121C2D3×Dic2112yesdirect product factor
122C2C2×D3×D2111yescharacteristic
subgroupG/H
center, hypercenterC22D3×D21
commutator, hypocenterC32×C7C22×C4
FrattiniC2C2×D3×D21
Fitting, socleC22×C32×C7C22
prime radicalC22×C3×D3×C7C2
cosocleC2×C32×C7C23
LCSG ▷ C32×C7
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. C2×C3⋊Dic21C2semidirect
3. C2×C3×Dic21C2semidirect
4. D3×Dic21C2direct (N × H)
8. C2×C3×D3×C7C4semidirect
10. C3⋊Dic21C22semidirect
11. C3×Dic21C22semidirect
18. C2×Dic21D3direct (N × H)
22. C2×C32×C7C2×C4semidirect
24. C3×D3×C7C2×C4semidirect
31. C2×D3×C7Dic3semidirect
36. Dic21C2×D3direct (N × H)
42. C32×C7C22×C4semidirect
52. C2×C3×C7C4×D3semidirect
53. C2×C3×C7C2×Dic3semidirect
56. D3×C7C2×Dic3semidirect
58. C2×C3×D3Dic7semidirect
77. C3×C7C2×C4×D3semidirect
78. C3×C7C22×Dic3semidirect
79. C2×C32C2×Dic7semidirect
81. C3×D3C2×Dic7semidirect
84. C2×C7D3×Dic3semidirect
91. C2×D3Dic21direct (N × H)
98. C32C22×Dic7semidirect
103. C7C2×D3×Dic3semidirect
107. C2×C3D3×Dic7semidirect
108. C2×C3C2×Dic21semidirect
111. D3C2×Dic21direct (N × H)
118. C3C2×D3×Dic7semidirect
119. C3C22×Dic21semidirect
121. C2D3×Dic21direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×C72
C2×C3⋊Dic212
C2×C3×Dic212
D3×Dic212
C22×Dic213
C2×D3×Dic73
C2×D3×Dic37