Finite Group Databasebeta

← C23×(C3⋊D3)⋊D7 #72246708

Subgroups — C23×(C3⋊D3)⋊D7 #72246708

Order 2016.

3126 conjugacy classes of subgroups; only the 639 normal subgroups are shown.

normal subgroups only

This group has 3126 conjugacy classes of subgroups — too many to draw. Only its 639 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
1C23×C7×C3⋊D3C211yesmaximal, characteristic, complemented
2C23×C3×D21C212yesmaximal, complemented
3C22×(C3⋊D3)⋊D7C2128yesmaximal, direct product factor
4C23×D3×D7—32nomaximal
5C23×C32×C7C2211yescharacteristic, complemented
6C22×C7×C3⋊D3C22114yescomplemented
7C22×C3×D21C22128yescomplemented
8C2×(C3⋊D3)⋊D7C221112yesdirect product factor
9C23×D21D312yescomplemented
10C23×D3×C7—32no—
11C23×D3×C7—61no—
12C23×C3×D7—32no—
13C22×D3×D7—356no—
14C23×D32—71nomaximal, Hall
15C22×C32×C7C2317yescomplemented
16C2×C7×C3⋊D3C23128yescomplemented
17C2×C3×D21C23156yescomplemented
18(C3⋊D3)⋊D7C23164yesdirect product factor
19C24×D7—91noHall
20C23×C3×C7—21no—
21C23×C3×C7C2×D312yescomplemented
22C22×D21C2×D3128yescomplemented
23C22×D3×C7—328no—
24C22×D3×C7—614no—
25C22×C3×D7—328no—
26C2×D3×D7—3224no—
27C23×C3⋊D3D711yescharacteristic, complemented
28C23×C3×D3—72no—
29C22×D32—728no—
30C2×C32×C7C2417yescomplemented
31C7×C3⋊D3C2418yescomplemented
32C3×D21C24116yescomplemented
33C24×C7—91no—
34C23×D7—32no—
35C23×D7—928no—
36C24×D3—212no—
37C22×C3×C7—27no—
38C22×C3×C7C22×D3114yescomplemented
39C2×D21C22×D3156yescomplemented
40C2×D3×C7—356no—
41C2×D3×C7—628no—
42C2×C3×D7—356no—
43D3×D7—3128no—
44C23×C32C2×D711yescharacteristic, complemented
45C22×C3⋊D3C2×D7114yescomplemented
46C22×C3×D3—728no—
47C2×D32—7112no—
48C32×C7C2511yescharacteristic, complemented, Hall
49C23×C7—914no—
50C23×C7D3211yescharacteristic, complemented
51C22×D7—328no—
52C22×D7—9112no—
53C24×C3—212no—
54C23×D3—32no—
55C23×D3—61no—
56C23×D3—72no—
57C23×D3—2156no—
58C2×C3×C7—27no—
59C2×C3×C7C23×D3114yescomplemented
60D21C23×D3116yescomplemented
61C3×D7—316no—
62D3×C7—316no—
63D3×C7—68no—
64C22×C32C22×D717yescomplemented
65C2×C3⋊D3C22×D7128yescomplemented
66C2×C3×D3—756no—
67D32—764no—
68C25—631noSylow
69C22×C7—928no—
70C22×C7C2×D3217yescomplemented
71C2×D7—356no—
72C2×D7—964no—
73C23×C3—21no—
74C23×C3—2128no—
75C23×C3D3×D712yescomplemented
76C22×D3—328no—
77C22×D3—614no—
78C22×D3—728no—
79C22×D3—21224no—
80C3×C7—21no—
81C3×C7C24×D312yescomplemented
82C2×C32C23×D717yescomplemented
83C3⋊D3C23×D718yescomplemented
84C3×D3—716no—
85C24—91no—
86C24—212no—
87C24—6328no—
88C2×C7—98no—
89C2×C7C22×D3217yescomplemented
90D7—316no—
91C22×C3—27no—
92C22×C3—2156no—
93C22×C3C2×D3×D7114yescomplemented
94C2×D3—356no—
95C2×D3—628no—
96C2×D3—756no—
97C2×D3—21128no—
98C32C24×D711yescharacteristic, complemented, Sylow
99C23—914no—
100C23—2128no—
101C23—63112no—
102C23(C3⋊D3)⋊D711yescharacteristic, direct product factor
103C7C23×D3211yescharacteristic, complemented, Sylow
104C2×C3—27no—
105C2×C3—2116no—
106C2×C3C22×D3×D7114yescomplemented
107D3—316no—
108D3—68no—
109D3—716no—
110C22—928no—
111C22—2156no—
112C22—6364no—
113C22C2×(C3⋊D3)⋊D717yesdirect product factor
114C3—21no—
115C3C23×D3×D712yescomplemented
116C2—98no—
117C2—2116no—
118C2C22×(C3⋊D3)⋊D717yesdirect product factor
subgroupG/H
center, hypercenterC23(C3⋊D3)⋊D7
commutator, cosocle, hypocenterC32×C7C25
FrattiniC1G
Fitting, socleC23×C32×C7C22
LCSG ▷ C32×C7
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C23×C7×C3⋊D3C2semidirect
2. C23×C3×D21C2semidirect
3. C22×(C3⋊D3)⋊D7C2direct (N × H)
5. C23×C32×C7C22semidirect
6. C22×C7×C3⋊D3C22semidirect
7. C22×C3×D21C22semidirect
8. C2×(C3⋊D3)⋊D7C22direct (N × H)
9. C23×D21D3semidirect
15. C22×C32×C7C23semidirect
16. C2×C7×C3⋊D3C23semidirect
17. C2×C3×D21C23semidirect
18. (C3⋊D3)⋊D7C23direct (N × H)
21. C23×C3×C7C2×D3semidirect
22. C22×D21C2×D3semidirect
27. C23×C3⋊D3D7semidirect
30. C2×C32×C7C24semidirect
31. C7×C3⋊D3C24semidirect
32. C3×D21C24semidirect
38. C22×C3×C7C22×D3semidirect
39. C2×D21C22×D3semidirect
44. C23×C32C2×D7semidirect
45. C22×C3⋊D3C2×D7semidirect
48. C32×C7C25semidirect
50. C23×C7D32semidirect
59. C2×C3×C7C23×D3semidirect
60. D21C23×D3semidirect
64. C22×C32C22×D7semidirect
65. C2×C3⋊D3C22×D7semidirect
70. C22×C7C2×D32semidirect
75. C23×C3D3×D7semidirect
81. C3×C7C24×D3semidirect
82. C2×C32C23×D7semidirect
83. C3⋊D3C23×D7semidirect
89. C2×C7C22×D32semidirect
93. C22×C3C2×D3×D7semidirect
98. C32C24×D7semidirect
102. C23(C3⋊D3)⋊D7direct (N × H)
103. C7C23×D32semidirect
106. C2×C3C22×D3×D7semidirect
113. C22C2×(C3⋊D3)⋊D7direct (N × H)
115. C3C23×D3×D7semidirect
118. C2C22×(C3⋊D3)⋊D7direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C7×C3⋊D32
C23×C3×D212
C22×(C3⋊D3)⋊D72
C23×D3×D73
C23×D327