Finite Group Databasebeta

← C2×Dic3×D21 #11759614

Subgroups — C2×Dic3×D21 #11759614

Order 1008.

232 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 82 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×D21C211yesmaximal, characteristic
2C2×C3⋊Dic21C211yesmaximal, characteristic, complemented
3C2×C3×C7×Dic3C211yesmaximal, characteristic, complemented
4Dic3×D21C214yesmaximal, direct product factor
5C2×C4×D21—31nomaximal
6C2×Dic3×D7—31nomaximal
7C22×C32×C7C2211yescharacteristic
8C2×C3×D21C414yescomplemented
9C2×C3×D21C2212yes—
10C3⋊Dic21C2212yescomplemented
11C3×C7×Dic3C2212yescomplemented
12C22×D21D311yescharacteristic
13C22×C3×D7—31no—
14C2×C3×C4×C7—31no—
15C2×Dic21—31no—
16C2×Dic21—31no—
17C2×Dic21—61no—
18C4×D21—34no—
19C2×C7×Dic3D311yescharacteristic, complemented
20Dic3×D7—34no—
21C2×D3×Dic3—71nomaximal, Hall
22C2×C32×C7C2×C412yescomplemented
23C2×C32×C7C2311yescharacteristic
24C3×D21C2×C414yescomplemented
25C2×C4×D7—91noHall
26C22×C3×C7—21no—
27C22×C3×C7C2×D311yescharacteristic
28C22×C3×C7C2×D311yescharacteristic
29C2×D21Dic314yesdirect product factor
30C2×D21C2×D312yes—
31C2×C3×D7—34no—
32C2×C3×D7—32no—
33C3×C4×C7—32no—
34Dic21—32no—
35Dic21—32no—
36Dic21—62no—
37C7×Dic3C2×D312yescomplemented
38C22×C3×D3—71no—
39C2×C3⋊Dic3—71no—
40C2×C3×Dic3D711yescharacteristic, complemented
41D3×Dic3—74no—
42C32×C7C22×C411yescharacteristic, complemented, Hall
43C22×D7—31no—
44C2×C4×C7—31no—
45C2×Dic7—91no—
46C4×D7—94no—
47C22×Dic3—211no—
48C2×C4×D3—211no—
49C2×C3×C7—22no—
50C2×C3×C7—21no—
51C2×C3×C7C4×D312yescomplemented
52C2×C3×C7C2×Dic312yescomplemented
53C2×C3×C7C22×D311yescharacteristic
54C2×C3×C7C22×D311yescharacteristic
55D21C2×Dic314yesdirect product factor
56C3×D7—34no—
57C22×C32C2×D711yescharacteristic
58C2×C3×D3—74no—
59C2×C3×D3—72no—
60C3⋊Dic3—72no—
61C3×Dic3C2×D712yescomplemented
62C22×C7D3211yescharacteristic
63C2×D7—34no—
64C2×D7—32no—
65C4×C7—32no—
66Dic7—92no—
67C23×C3—211no—
68C22×D3—71no—
69C2×C3×C4—31no—
70C2×Dic3—211no—
71C2×Dic3—211no—
72C2×Dic3—214no—
73C2×Dic3—421no—
74C2×Dic3D2111yescharacteristic, direct product factor
75C4×D3—214no—
76C3×C7—21no—
77C3×C7C2×C4×D311yescharacteristic, complemented
78C3×C7C22×Dic311yescharacteristic, complemented
79C2×C32C4×D712yescomplemented
80C2×C32C22×D711yescharacteristic
81C3×D3—74no—
82C22×C4—631noSylow
83C2×C7D3×Dic312yescomplemented
84C2×C7C2×D3211yescharacteristic
85D7—34no—
86C22×C3—21no—
87C22×C3—214no—
88C22×C3—212no—
89C22×C3D3×D711yescharacteristic
90C22×C3C2×D2111yescharacteristic
91C2×D3—74no—
92C2×D3—72no—
93C3×C4—32no—
94Dic3—212no—
95Dic3—212no—
96Dic3—422no—
97Dic3C2×D2112yesdirect product factor
98C32C2×C4×D711yescharacteristic, complemented, Sylow
99C23—211no—
100C2×C4—31no—
101C2×C4—634no—
102C2×C4—631no—
103C7C2×D3×Dic311yescharacteristic, complemented, Sylow
104C2×C3—22no—
105C2×C3—21no—
106C2×C3—214no—
107C2×C3Dic3×D712yescomplemented
108C2×C3C4×D2112yescomplemented
109C2×C3C2×D3×D711yescharacteristic
110C2×C3C22×D2111yescharacteristic
111D3—74no—
112C22—214no—
113C22—212no—
114C22D3×D2111yescharacteristic
115C4—32no—
116C4—632no—
117C3—21no—
118C3C2×Dic3×D711yescharacteristic, complemented
119C3C2×C4×D2111yescharacteristic, complemented
120C2—214no—
121C2Dic3×D2112yesdirect product factor
122C2C2×D3×D2111yescharacteristic
subgroupG/H
center, hypercenterC22D3×D21
commutator, hypocenterC32×C7C22×C4
FrattiniC2C2×D3×D21
Fitting, socleC22×C32×C7C22
prime radicalC22×C3×D21C2
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×C7×Dic3C2semidirect
4. Dic3×D21C2direct (N × H)
8. C2×C3×D21C4semidirect
10. C3⋊Dic21C22semidirect
11. C3×C7×Dic3C22semidirect
19. C2×C7×Dic3D3semidirect
22. C2×C32×C7C2×C4semidirect
24. C3×D21C2×C4semidirect
29. C2×D21Dic3direct (N × H)
37. C7×Dic3C2×D3semidirect
40. C2×C3×Dic3D7semidirect
42. C32×C7C22×C4semidirect
51. C2×C3×C7C4×D3semidirect
52. C2×C3×C7C2×Dic3semidirect
55. D21C2×Dic3direct (N × H)
61. C3×Dic3C2×D7semidirect
74. C2×Dic3D21direct (N × H)
77. C3×C7C2×C4×D3semidirect
78. C3×C7C22×Dic3semidirect
79. C2×C32C4×D7semidirect
83. C2×C7D3×Dic3semidirect
97. Dic3C2×D21direct (N × H)
98. C32C2×C4×D7semidirect
103. C7C2×D3×Dic3semidirect
107. C2×C3Dic3×D7semidirect
108. C2×C3C4×D21semidirect
118. C3C2×Dic3×D7semidirect
119. C3C2×C4×D21semidirect
121. C2Dic3×D21direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D212
C2×C3⋊Dic212
C2×C3×C7×Dic32
Dic3×D212
C2×C4×D213
C2×Dic3×D73
C2×D3×Dic37