Finite Group Databasebeta

← C2×#543×C113 #28388252

Subgroups — C2×#543×C113 #28388252

Order 14464.

1296 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#543×C113C2116yesmaximal, direct product factor
2C2×C22⋊Q8×C113C2112yesmaximal, complemented
3C22×C22⋊C4×C113C213yesmaximal
4C25×C113C2211yescharacteristic
5C22×Q8×C113C2214yescomplemented
6C23×C4×C113C2216yes—
7C22⋊Q8×C113C22196yescomplemented
8C2×C4⋊C4×C113C22112yescomplemented
9C2×C22⋊C4×C113C22112yes—
10C2×C22⋊C4×C113C22124yes—
11C24×C113—44no—
12C24×C113Q818yescomplemented
13C24×C113C2313yes—
14C24×C113C2314yes—
15C2×Q8×C113—48no—
16C2×Q8×C113C23116yescomplemented
17C22×C4×C113—412no—
18C22×C4×C113C23112yes—
19C22×C4×C113C23124yes—
20C4⋊C4×C113C23148yescomplemented
21C22⋊C4×C113C23148yes—
22C23×C113—212no—
23C23×C113—416no—
24C23×C113—48no—
25C23×C113C2×Q8112yes—
26C23×C113C2×Q8116yescomplemented
27C23×C113C2416yes—
28C23×C113C2411yescharacteristic
29Q8×C113—416no—
30C2×C4×C113—224no—
31C2×C4×C113—424no—
32C2×C4×C113C24124yes—
33C22×C113—224no—
34C22×C113—212no—
35C22×C113—416no—
36C22×C113C22×Q8112yes—
37C22×C113C22×Q812yes—
38C22×C113H(5,𝔽2)14yes—
39C22×C113C2511yescharacteristic
40C4×C113—224no—
41C2×C113—212no—
42C2×C113#54314yesdirect product factor
43C2×C113C23×Q811yescharacteristic
44C2×C113C2×H(5,𝔽2)12yes—
45C2×#543C11311yesmaximal, characteristic, direct product factor, Sylow
46C113C2×#54311yescharacteristic, direct product factor, Sylow
47#543C2×C113116yesdirect product factor
48C2×C22⋊Q8C2×C113112yescomplemented
49C22×C22⋊C4C2×C11313yes—
50C25C22×C11311yescharacteristic
51C22×Q8C22×C11314yescomplemented
52C23×C4C22×C11316yes—
53C22⋊Q8C22×C113196yescomplemented
54C2×C4⋊C4C22×C113112yescomplemented
55C2×C22⋊C4C22×C113112yes—
56C2×C22⋊C4C22×C113124yes—
57C24—44no—
58C24Q8×C11318yescomplemented
59C24C23×C11313yes—
60C24C23×C11314yes—
61C2×Q8—48no—
62C2×Q8C23×C113116yescomplemented
63C22×C4—412no—
64C22×C4C23×C113112yes—
65C22×C4C23×C113124yes—
66C4⋊C4C23×C113148yescomplemented
67C22⋊C4C23×C113148yes—
68C23—212no—
69C23—416no—
70C23—48no—
71C23C2×Q8×C113112yes—
72C23C2×Q8×C113116yescomplemented
73C23C24×C11316yes—
74C23C24×C11311yescharacteristic
75Q8—416no—
76C2×C4—224no—
77C2×C4—424no—
78C2×C4C24×C113124yes—
79C22—224no—
80C22—212no—
81C22—416no—
82C22C22×Q8×C113112yes—
83C22C22×Q8×C11312yes—
84C22H(5,𝔽2)×C11314yes—
85C22C25×C11311yescharacteristic
86C4—224no—
87C2—212no—
88C2#543×C11314yesdirect product factor
89C2C23×Q8×C11311yescharacteristic
90C2C2×H(5,𝔽2)×C11312yes—
subgroupG/H
center, socleC23×C113C24
commutator, Frattini, cosocleC22C25×C113
prime radicalC25×C113C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. #543×C113C2direct (N × H)
2. C2×C22⋊Q8×C113C2semidirect
5. C22×Q8×C113C22semidirect
7. C22⋊Q8×C113C22semidirect
8. C2×C4⋊C4×C113C22semidirect
12. C24×C113Q8semidirect
16. C2×Q8×C113C23semidirect
20. C4⋊C4×C113C23semidirect
26. C23×C113C2×Q8semidirect
42. C2×C113#543direct (N × H)
45. C2×#543C113direct (N × H)
46. C113C2×#543direct (N × H)
47. #543C2×C113direct (N × H)
48. C2×C22⋊Q8C2×C113semidirect
51. C22×Q8C22×C113semidirect
53. C22⋊Q8C22×C113semidirect
54. C2×C4⋊C4C22×C113semidirect
58. C24Q8×C113semidirect
62. C2×Q8C23×C113semidirect
66. C4⋊C4C23×C113semidirect
72. C23C2×Q8×C113semidirect
88. C2#543×C113direct (N × H)

Maximal subgroups

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

subgroupindex
#543×C1132
C2×C22⋊Q8×C1132
C22×C22⋊C4×C1132
C2×#543113