Finite Group Databasebeta

← #14558369

Subgroups — #14558369

Order 2368.

810 conjugacy classes of subgroups; only the 443 normal subgroups are shown.

normal subgroups only

This group has 810 conjugacy classes of subgroups — too many to draw. Only its 443 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#11924584C212yesmaximal, complemented
2#11924583C214yesmaximal, complemented
3#11924582C214yesmaximal, complemented
4#11924581C216yesmaximal, complemented
5C2×#10596962C216yesmaximal, complemented
6#41×D37C218yesmaximal, complemented
7C2×#41×C37C211yesmaximal, characteristic, complemented
8#41×C37C2214yescomplemented
9#41×C37C2214yescomplemented
10C2×Q8×C37C2211yescharacteristic, complemented
11C2×D4×C37C2213yescomplemented
12C22×C4×C37C2213yescomplemented
13C2×C22⋊D37C22112yescomplemented
14#10596966C2218yescomplemented
15Q8×D37C2218yescomplemented
16#10596964C22124yescomplemented
17D4×D37C22124yescomplemented
18#10596962C22112yescomplemented
19#10596962C2214yescomplemented
20#10596962C22112yescomplemented
21#10596962C22112yescomplemented
22C2×D148C2216yescomplemented
23C2×C4×D37C22112yescomplemented
24C2×Dic74C2216yescomplemented
25C23×C37C2313yes—
26C22×D37C23112yes—
27Q8×C37C2314yes—
28D4×C37C23112yes—
29C2×C4×C37C2316yes—
30C2×C4×C37C2316yes—
31C2×C4×C37C2311yescharacteristic
32C2×C4×C37C2313yes—
33C22⋊D37C2318yes—
34C22⋊D37C23124yes—
35C2×Dic37C23112yes—
36D148C2314yes—
37D148C23112yes—
38C4×D37C2318yes—
39C4×D37C23124yes—
40Dic74C2314yes—
41Dic74C23112yes—
42C22×C37—43no—
43C22×C37C2416yes—
44C22×C37C2411yescharacteristic
45C2×D37—412no—
46C2×D37C2418yes—
47C4×C37C2411yescharacteristic
48C4×C37C2416yes—
49C4×C37C2411yescharacteristic
50Dic37C2418yes—
51C2×C37—26no—
52C2×C37—21no—
53C2×C37C2511yescharacteristic
54D37—28no—
55#585—371nomaximal, Sylow
56C37#58511yescharacteristic, complemented, Sylow
572−1+4—374no—
582−1+4—372no—
59H(5,𝔽2)—374no—
60H(5,𝔽2)—376no—
61C2×#41—378no—
62C2×#41—376no—
63C2×#41D3711yescharacteristic, complemented
64#41—378no—
65#41—3724no—
66#41—3712no—
67#41—374no—
68#41—3712no—
69#41—3712no—
70#41C2×D3714yescomplemented
71#41C2×D3714yescomplemented
72C2×Q8—378no—
73C2×Q8—376no—
74C2×Q8C2×D3711yescharacteristic, complemented
75C2×D4—3712no—
76C2×D4—3724no—
77C2×D4—376no—
78C2×D4C2×D3713yescomplemented
79C22×C4—3712no—
80C22×C4C2×D3713yescomplemented
81C23—3712no—
82C23C22×D3713yes—
83Q8—3712no—
84Q8—374no—
85Q8C22×D3714yes—
86D4—3724no—
87D4—378no—
88D4—3712no—
89D4—374no—
90D4C22×D37112yes—
91C2×C4—3712no—
92C2×C4—3724no—
93C2×C4—378no—
94C2×C4C22×D3716yes—
95C2×C4C22×D3713yes—
96C2×C4C22×D3716yes—
97C2×C4C22×D3711yescharacteristic
98C22—43no—
99C22—378no—
100C22—14812no—
101C22C23×D3716yes—
102C22C23×D3711yescharacteristic
103C4—378no—
104C4C23×D3716yes—
105C4C23×D3711yescharacteristic
106C4C23×D3711yescharacteristic
107C2—21no—
108C2—26no—
109C2—748no—
110C2C24×D3711yescharacteristic
subgroupG/H
centerC4C23×D37
commutator, socle, cosocleC2×C37C25
FrattiniC2C24×D37
FittingC2×#41×C37C2
hypercenterC2×#41D37
hypocenterC37#585
LCSG ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #11924584C2semidirect
2. #11924583C2semidirect
3. #11924582C2semidirect
4. #11924581C2semidirect
5. C2×#10596962C2semidirect
6. #41×D37C2semidirect
7. C2×#41×C37C2semidirect
8. #41×C37C22semidirect
9. #41×C37C22semidirect
10. C2×Q8×C37C22semidirect
11. C2×D4×C37C22semidirect
12. C22×C4×C37C22semidirect
13. C2×C22⋊D37C22semidirect
14. #10596966C22semidirect
15. Q8×D37C22semidirect
16. #10596964C22semidirect
17. D4×D37C22semidirect
18. #10596962C22semidirect
19. #10596962C22semidirect
20. #10596962C22semidirect
21. #10596962C22semidirect
22. C2×D148C22semidirect
23. C2×C4×D37C22semidirect
24. C2×Dic74C22semidirect
56. C37#585semidirect
63. C2×#41D37semidirect
70. #41C2×D37semidirect
71. #41C2×D37semidirect
74. C2×Q8C2×D37semidirect
78. C2×D4C2×D37semidirect
80. C22×C4C2×D37semidirect

Maximal subgroups

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

subgroupindex
#119245842
#119245832
#119245822
#119245812
C2×#105969622
#41×D372
C2×#41×C372
#58537