Finite Group Databasebeta

← #14558341

Subgroups — #14558341

Order 2368.

258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 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
1#11924582C211yesmaximal, characteristic, complemented
2#11924567C213yesmaximal, complemented
3#11924561C213yesmaximal, complemented
4#11924556C213yesmaximal, complemented
5C2×#10596941C213yesmaximal, complemented
6#11924543C211yesmaximal, characteristic, complemented
72−1+4×C37C211yesmaximal, characteristic, complemented
8#41×C37—23no—
9#41×C37C2211yescharacteristic
10#41×C37C2213yescomplemented
11C2×Q8×C37—21no—
12C2×Q8×C37C2213yescomplemented
13#10596966—21no—
14D4×D37—23no—
15#10596962C2213yes—
16C2×D148C2213yes—
17#10596942C2213yescomplemented
18#10596941C2213yescomplemented
19#10596941C2216yescomplemented
20#10596940C2211yescharacteristic, complemented
21#10596939C2213yescomplemented
22#10596934C2213yescomplemented
23C2×#64436C2213yescomplemented
24C22×D37—23no—
25Q8×C37—23no—
26Q8×C37D411yescharacteristic
27Q8×C37C2313yes—
28D4×C37—23no—
29D4×C37D413yes—
30D4×C37C2311yescharacteristic
31C2×C4×C37—23no—
32C2×C4×C37—23no—
33C2×C4×C37C2313yes—
34C22⋊D37—23no—
35D148—23no—
36D148C2313yes—
37C4×D37—23no—
38Dic74C2311yescharacteristic
39#64436C2311yescharacteristic
40#64436C2313yes—
41C22×C37—21no—
42C22×C37C2×D413yes—
43C2×D37—23no—
44C2×D37—83no—
45C4×C37—23no—
46C4×C37C2×D413yes—
47C4×C37C2411yescharacteristic
48Dic37—21no—
49C2×C37—23no—
50C2×C37—41no—
51C2×C37C22×D411yescharacteristic
52D37—43no—
53#577—371nomaximal, Sylow
54C37#57711yescharacteristic, complemented, Sylow
552−1+4D3711yescharacteristic, complemented
56H(5,𝔽2)—371no—
57#137—373no—
58AGL(1,ℤ/8)—373no—
59#135—373no—
60C2×SD16—373no—
61#131—371no—
62#41—23no—
63#41—373no—
64#41—741no—
65#41C2×D3711yescharacteristic
66#41C2×D3713yescomplemented
67C2×Q8—21no—
68C2×Q8C2×D3713yescomplemented
69C2×D4—373no—
70C2×D4—743no—
71Q16—373no—
72SD16—373no—
73SD16—376no—
74SD16—371no—
75D8—373no—
76M16—373no—
77C2×C8—373no—
78C23—743no—
79Q8—23no—
80Q8—371no—
81Q8C22⋊D3711yescharacteristic
82Q8C22×D3713yes—
83D4—23no—
84D4—373no—
85D4—743no—
86D4—743no—
87D4C22⋊D3713yes—
88D4C22×D3711yescharacteristic
89C2×C4—23no—
90C2×C4—23no—
91C2×C4—743no—
92C2×C4C22×D3713yes—
93C8—371no—
94C8—373no—
95C22—21no—
96C22—2963no—
97C22—743no—
98C22C2×C22⋊D3713yes—
99C4—23no—
100C4—741no—
101C4C2×C22⋊D3713yes—
102C4C23×D3711yescharacteristic
103C2—23no—
104C2—41no—
105C2—1483no—
106C2C22×C22⋊D3711yescharacteristic
subgroupG/H
centerC2C22×C22⋊D37
commutator, cosocleC4×C37C24
FrattiniC4C23×D37
Fitting2−1+4×C37C2
socleC2×C37C22×D4
hypercenter2−1+4D37
hypocenterC37#577
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ #41 ◁ 2−1+4

Complements

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

NH ≅ G/Ntype
1. #11924582C2semidirect
2. #11924567C2semidirect
3. #11924561C2semidirect
4. #11924556C2semidirect
5. C2×#10596941C2semidirect
6. #11924543C2semidirect
7. 2−1+4×C37C2semidirect
10. #41×C37C22semidirect
12. C2×Q8×C37C22semidirect
17. #10596942C22semidirect
18. #10596941C22semidirect
19. #10596941C22semidirect
20. #10596940C22semidirect
21. #10596939C22semidirect
22. #10596934C22semidirect
23. C2×#64436C22semidirect
54. C37#577semidirect
55. 2−1+4D37semidirect
66. #41C2×D37semidirect
68. C2×Q8C2×D37semidirect

Maximal subgroups

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

subgroupindex
#119245822
#119245672
#119245612
#119245562
C2×#105969412
#119245432
2−1+4×C372
#57737