Finite Group Databasebeta

← C2×#26044229 #37554671

Subgroups — C2×#26044229 #37554671

Order 23488.

662 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 143 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×D367C211yesmaximal, characteristic, complemented
2C22×C22⋊D367C212yesmaximal, complemented
3#26044229C218yesmaximal, direct product factor
4C2×C22⋊Dic367C211yesmaximal, characteristic, complemented
5C2×(C2×D367)⋊C4C212yesmaximal, complemented
6C22×D4×C367C211yesmaximal, characteristic, complemented
7C23×D367—28no—
8C23×D367—24no—
9C23×D367C2212yes—
10C23×D367C2214yescomplemented
11C2×C22⋊D367—28no—
12C2×C22⋊D367C2218yescomplemented
13C22×Dic367C2212yescomplemented
14C22⋊Dic367C2214yescomplemented
15(C2×D367)⋊C4C2218yescomplemented
16C24×C367C2211yescharacteristic
17C24×C367C2211yescharacteristic, complemented
18C2×D4×C367—24no—
19C2×D4×C367C2214yescomplemented
20C22×C4×C367C2211yescharacteristic, complemented
21C22×D367—232no—
22C22×D367—24no—
23C22×D367—24no—
24C22×D367—28no—
25C22×D367—216no—
26C22×D367D418yescomplemented
27C22×D367C2314yes—
28C22⋊D367—216no—
29C2×Dic367—24no—
30C2×Dic367C2314yescomplemented
31C23×C367—24no—
32C23×C367—22no—
33C23×C367—24no—
34C23×C367D414yescomplemented
35C23×C367C2312yes—
36C23×C367C2311yescharacteristic
37C23×C367C2312yescomplemented
38D4×C367—28no—
39C2×C4×C367—22no—
40C2×C4×C367C2312yescomplemented
41C22×C367—28no—
42C22×C367—24no—
43C22×C367—22no—
44C22×C367—24no—
45C22×C367—44no—
46C22×C367C2×D414yes—
47C22×C367C2×D412yes—
48C22×C367C2×D414yescomplemented
49C22×C367C2411yescharacteristic
50C2×D367—232no—
51C2×D367—216no—
52C2×D367—24no—
53C2×D367—24no—
54C2×D367C2×D418yescomplemented
55C4×C367—22no—
56Dic367—24no—
57C2×C367—24no—
58C2×C367—42no—
59C2×C367#12014yescomplemented
60C2×C367C22×D412yes—
61C2×C367C22×D411yescharacteristic
62D367—28no—
63C367C2×#12011yescharacteristic, complemented, Sylow
64C2×#120—3671nomaximal, Sylow
65C25—3671no—
66C22×D4—3672no—
67C22×D4D36711yescharacteristic, complemented
68#120—3678no—
69C2×C22⋊C4—3671no—
70C2×C22⋊C4—3672no—
71C24—3672no—
72C24—3674no—
73C24—7348no—
74C24—7344no—
75C24C2×D36711yescharacteristic
76C24C2×D36711yescharacteristic, complemented
77C2×D4—24no—
78C2×D4—3678no—
79C2×D4—7348no—
80C2×D4C2×D36714yescomplemented
81C22×C4—3672no—
82C22×C4C2×D36711yescharacteristic, complemented
83C22⋊C4—3674no—
84C22⋊C4—3678no—
85C23—24no—
86C23—24no—
87C23—22no—
88C23—3678no—
89C23—3674no—
90C23—73416no—
91C23—73432no—
92C23—7344no—
93C23—7344no—
94C23—7348no—
95C23C22⋊D36714yescomplemented
96C23C22×D36712yes—
97C23C22×D36711yescharacteristic
98C23C22×D36712yescomplemented
99D4—28no—
100D4—73416no—
101C2×C4—22no—
102C2×C4—3674no—
103C2×C4—7344no—
104C2×C4C22×D36712yescomplemented
105C22—28no—
106C22—24no—
107C22—24no—
108C22—22no—
109C22—44no—
110C22—3678no—
111C22—73432no—
112C22—73416no—
113C22—7344no—
114C22—7344no—
115C22D4×D36714yes—
116C22C2×C22⋊D36712yes—
117C22C2×C22⋊D36714yescomplemented
118C22C23×D36711yescharacteristic
119C4—22no—
120C4—7344no—
121C2—24no—
122C2—42no—
123C2—7348no—
124C2#2604422914yesdirect product factor
125C2C2×D4×D36712yes—
126C2C22×C22⋊D36711yescharacteristic
subgroupG/H
centerC23C22×D367
commutator, cosocleC22×C367C24
FrattiniC22C23×D367
FittingC22×D4×C367C2
socleC23×C367C23
hypercenterC22×D4D367
hypocenterC367C2×#120
LCSG ▷ C22×C367 ▷ C367
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C24×D367C2semidirect
2. C22×C22⋊D367C2semidirect
3. #26044229C2direct (N × H)
4. C2×C22⋊Dic367C2semidirect
5. C2×(C2×D367)⋊C4C2semidirect
6. C22×D4×C367C2semidirect
10. C23×D367C22semidirect
12. C2×C22⋊D367C22semidirect
13. C22×Dic367C22semidirect
14. C22⋊Dic367C22semidirect
15. (C2×D367)⋊C4C22semidirect
17. C24×C367C22semidirect
19. C2×D4×C367C22semidirect
20. C22×C4×C367C22semidirect
26. C22×D367D4semidirect
30. C2×Dic367C23semidirect
34. C23×C367D4semidirect
37. C23×C367C23semidirect
40. C2×C4×C367C23semidirect
48. C22×C367C2×D4semidirect
54. C2×D367C2×D4semidirect
59. C2×C367#120semidirect
63. C367C2×#120semidirect
67. C22×D4D367semidirect
76. C24C2×D367semidirect
80. C2×D4C2×D367semidirect
82. C22×C4C2×D367semidirect
95. C23C22⋊D367semidirect
98. C23C22×D367semidirect
104. C2×C4C22×D367semidirect
117. C22C2×C22⋊D367semidirect
124. C2#26044229direct (N × H)

Maximal subgroups

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

subgroupindex
C24×D3672
C22×C22⋊D3672
#260442292
C2×C22⋊Dic3672
C2×(C2×D367)⋊C42
C22×D4×C3672
C2×#120367