Finite Group Databasebeta

← C23×D3×Dic7 #13062282

Subgroups — C23×D3×Dic7 #13062282

Order 1344.

2724 conjugacy classes of subgroups; only the 1240 normal subgroups are shown.

normal subgroups only

This group has 2724 conjugacy classes of subgroups — too many to draw. Only its 1240 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
1C24×D3×C7C211yesmaximal, characteristic
2C23×Dic21C211yesmaximal, characteristic, complemented
3C23×C3×Dic7C211yesmaximal, characteristic, complemented
4C22×D3×Dic7C2128yesmaximal, direct product factor
5C24×Dic7—31nomaximal, Hall
6C24×C3×C7C2211yescharacteristic
7C23×D3×C7C4116yescomplemented
8C23×D3×C7C22114yes—
9C22×Dic21C22114yescomplemented
10C22×C3×Dic7C22114yescomplemented
11C2×D3×Dic7C221112yesdirect product factor
12C25×C7—31no—
13C23×Dic7—31no—
14C23×Dic7—328no—
15C23×Dic7D311yescharacteristic, direct product factor
16C23×C4×D3—71nomaximal, Hall
17C23×C3×C7C2×C418yescomplemented
18C23×C3×C7C2317yes—
19C22×D3×C7C2×C41112yescomplemented
20C22×D3×C7C23128yes—
21C2×Dic21C23128yescomplemented
22C2×C3×Dic7C23128yescomplemented
23D3×Dic7C23164yesdirect product factor
24C24×C7—316no—
25C24×C7—314no—
26C24×C7C2×D311yescharacteristic
27C22×Dic7—314no—
28C22×Dic7—3112no—
29C22×Dic7C2×D3114yesdirect product factor
30C24×D3D711yescharacteristic
31C23×C3×C4—71no—
32C23×Dic3—71no—
33C22×C4×D3—728no—
34C22×C3×C7C22×C4128yescomplemented
35C22×C3×C7C2417yes—
36C2×D3×C7C22×C41112yescomplemented
37C2×D3×C7C2418yes—
38Dic21C2418yescomplemented
39C3×Dic7C2418yescomplemented
40C24×C4—211noSylow
41C23×C7—3112no—
42C23×C7—328no—
43C23×C7C4×D318yescomplemented
44C23×C7C22×D317yes—
45C2×Dic7—328no—
46C2×Dic7—364no—
47C2×Dic7C22×D3128yesdirect product factor
48C24×C3C2×D711yescharacteristic
49C23×D3Dic7116yesdirect product factor
50C23×D3C2×D7114yes—
51C22×C3×C4—714no—
52C22×Dic3—714no—
53C2×C4×D3—7112no—
54C2×C3×C7C23×C4114yescomplemented
55C2×C3×C7C2511yescharacteristic
56D3×C7C23×C4116yescomplemented
57C25—31no—
58C23×C4—71no—
59C23×C4—2128no—
60C23×C4—211no—
61C22×C7—3112no—
62C22×C7—38no—
63C22×C7C2×C4×D3128yescomplemented
64C22×C7C23×D317yes—
65Dic7—38no—
66Dic7C23×D318yesdirect product factor
67C23×C3C2×Dic718yescomplemented
68C23×C3C22×D717yes—
69C22×D3C2×Dic71112yesdirect product factor
70C22×D3C22×D7128yes—
71C2×C3×C4—728no—
72C2×Dic3—728no—
73C4×D3—764no—
74C3×C7C24×C411yescharacteristic, complemented, Hall
75C24—316no—
76C24—314no—
77C24D3×D711yescharacteristic
78C22×C4—714no—
79C22×C4—21112no—
80C22×C4—2114no—
81C2×C7—316no—
82C2×C7C22×C4×D3114yescomplemented
83C2×C7C24×D311yescharacteristic
84C22×C3C22×Dic7128yescomplemented
85C22×C3C23×D717yes—
86C2×D3C22×Dic71112yesdirect product factor
87C2×D3C23×D718yes—
88C3×C4—78no—
89Dic3—78no—
90C23—3112no—
91C23—328no—
92C23D3×Dic718yesdirect product factor
93C23C2×D3×D717yes—
94C2×C4—728no—
95C2×C4—2164no—
96C2×C4—2128no—
97C7C23×C4×D311yescharacteristic, complemented, Sylow
98C2×C3C23×Dic7114yescomplemented
99C2×C3C24×D711yescharacteristic
100D3C23×Dic7116yesdirect product factor
101C22—3112no—
102C22—38no—
103C22C2×D3×Dic7128yesdirect product factor
104C22C22×D3×D717yes—
105C4—78no—
106C4—218no—
107C3C24×Dic711yescharacteristic, complemented, Sylow
108C2—316no—
109C2C22×D3×Dic7114yesdirect product factor
110C2C23×D3×D711yescharacteristic
subgroupG/H
center, hypercenterC24D3×D7
commutator, hypocenterC3×C7C24×C4
FrattiniC2C23×D3×D7
Fitting, socleC24×C3×C7C22
prime radicalC24×D3×C7C2
cosocleC2×C3×C7C25
LCSG ▷ C3×C7
UCSC1 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C23×Dic21C2semidirect
3. C23×C3×Dic7C2semidirect
4. C22×D3×Dic7C2direct (N × H)
7. C23×D3×C7C4semidirect
9. C22×Dic21C22semidirect
10. C22×C3×Dic7C22semidirect
11. C2×D3×Dic7C22direct (N × H)
15. C23×Dic7D3direct (N × H)
17. C23×C3×C7C2×C4semidirect
19. C22×D3×C7C2×C4semidirect
21. C2×Dic21C23semidirect
22. C2×C3×Dic7C23semidirect
23. D3×Dic7C23direct (N × H)
29. C22×Dic7C2×D3direct (N × H)
34. C22×C3×C7C22×C4semidirect
36. C2×D3×C7C22×C4semidirect
38. Dic21C24semidirect
39. C3×Dic7C24semidirect
43. C23×C7C4×D3semidirect
47. C2×Dic7C22×D3direct (N × H)
49. C23×D3Dic7direct (N × H)
54. C2×C3×C7C23×C4semidirect
56. D3×C7C23×C4semidirect
63. C22×C7C2×C4×D3semidirect
66. Dic7C23×D3direct (N × H)
67. C23×C3C2×Dic7semidirect
69. C22×D3C2×Dic7direct (N × H)
74. C3×C7C24×C4semidirect
82. C2×C7C22×C4×D3semidirect
84. C22×C3C22×Dic7semidirect
86. C2×D3C22×Dic7direct (N × H)
92. C23D3×Dic7direct (N × H)
97. C7C23×C4×D3semidirect
98. C2×C3C23×Dic7semidirect
100. D3C23×Dic7direct (N × H)
103. C22C2×D3×Dic7direct (N × H)
107. C3C24×Dic7semidirect
109. C2C22×D3×Dic7direct (N × H)

Maximal subgroups

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

subgroupindex
C24×D3×C72
C23×Dic212
C23×C3×Dic72
C22×D3×Dic72
C24×Dic73
C23×C4×D37