Finite Group Databasebeta

← #14583735

Subgroups — #14583735

Order 2752.

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#13063373C212yesmaximal, complemented
2#13063372C214yesmaximal, complemented
3#13063371C214yesmaximal, complemented
4#13063370C216yesmaximal, complemented
5C2×#10621898C216yesmaximal, complemented
6#41×D43C218yesmaximal, complemented
7C2×#41×C43C211yesmaximal, characteristic, complemented
8#41×C43C2214yescomplemented
9#41×C43C2214yescomplemented
10C2×Q8×C43C2211yescharacteristic, complemented
11C2×D4×C43C2213yescomplemented
12C22×C4×C43C2213yescomplemented
13C2×C22⋊D43C22112yescomplemented
14#10621902C2218yescomplemented
15Q8×D43C2218yescomplemented
16#10621900C22124yescomplemented
17D4×D43C22124yescomplemented
18#10621898C22112yescomplemented
19#10621898C2214yescomplemented
20#10621898C22112yescomplemented
21#10621898C22112yescomplemented
22C2×D172C2216yescomplemented
23C2×C4×D43C22112yescomplemented
24C2×Dic86C2216yescomplemented
25C23×C43C2313yes—
26C22×D43C23112yes—
27Q8×C43C2314yes—
28D4×C43C23112yes—
29C2×C4×C43C2316yes—
30C2×C4×C43C2316yes—
31C2×C4×C43C2311yescharacteristic
32C2×C4×C43C2313yes—
33C22⋊D43C2318yes—
34C22⋊D43C23124yes—
35C2×Dic43C23112yes—
36D172C2314yes—
37D172C23112yes—
38C4×D43C2318yes—
39C4×D43C23124yes—
40Dic86C2314yes—
41Dic86C23112yes—
42C22×C43—43no—
43C22×C43C2416yes—
44C22×C43C2411yescharacteristic
45C2×D43—412no—
46C2×D43C2418yes—
47C4×C43C2411yescharacteristic
48C4×C43C2416yes—
49C4×C43C2411yescharacteristic
50Dic43C2418yes—
51C2×C43—26no—
52C2×C43—21no—
53C2×C43C2511yescharacteristic
54D43—28no—
55#585—431nomaximal, Sylow
56C43#58511yescharacteristic, complemented, Sylow
572−1+4—434no—
582−1+4—432no—
59H(5,𝔽2)—434no—
60H(5,𝔽2)—436no—
61C2×#41—438no—
62C2×#41—436no—
63C2×#41D4311yescharacteristic, complemented
64#41—438no—
65#41—4324no—
66#41—4312no—
67#41—434no—
68#41—4312no—
69#41—4312no—
70#41C2×D4314yescomplemented
71#41C2×D4314yescomplemented
72C2×Q8—438no—
73C2×Q8—436no—
74C2×Q8C2×D4311yescharacteristic, complemented
75C2×D4—4312no—
76C2×D4—4324no—
77C2×D4—436no—
78C2×D4C2×D4313yescomplemented
79C22×C4—4312no—
80C22×C4C2×D4313yescomplemented
81C23—4312no—
82C23C22×D4313yes—
83Q8—4312no—
84Q8—434no—
85Q8C22×D4314yes—
86D4—4324no—
87D4—438no—
88D4—4312no—
89D4—434no—
90D4C22×D43112yes—
91C2×C4—4312no—
92C2×C4—4324no—
93C2×C4—438no—
94C2×C4C22×D4316yes—
95C2×C4C22×D4313yes—
96C2×C4C22×D4316yes—
97C2×C4C22×D4311yescharacteristic
98C22—43no—
99C22—438no—
100C22—17212no—
101C22C23×D4316yes—
102C22C23×D4311yescharacteristic
103C4—438no—
104C4C23×D4316yes—
105C4C23×D4311yescharacteristic
106C4C23×D4311yescharacteristic
107C2—21no—
108C2—26no—
109C2—868no—
110C2C24×D4311yescharacteristic
subgroupG/H
centerC4C23×D43
commutator, socle, cosocleC2×C43C25
FrattiniC2C24×D43
FittingC2×#41×C43C2
hypercenterC2×#41D43
hypocenterC43#585
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #13063373C2semidirect
2. #13063372C2semidirect
3. #13063371C2semidirect
4. #13063370C2semidirect
5. C2×#10621898C2semidirect
6. #41×D43C2semidirect
7. C2×#41×C43C2semidirect
8. #41×C43C22semidirect
9. #41×C43C22semidirect
10. C2×Q8×C43C22semidirect
11. C2×D4×C43C22semidirect
12. C22×C4×C43C22semidirect
13. C2×C22⋊D43C22semidirect
14. #10621902C22semidirect
15. Q8×D43C22semidirect
16. #10621900C22semidirect
17. D4×D43C22semidirect
18. #10621898C22semidirect
19. #10621898C22semidirect
20. #10621898C22semidirect
21. #10621898C22semidirect
22. C2×D172C22semidirect
23. C2×C4×D43C22semidirect
24. C2×Dic86C22semidirect
56. C43#585semidirect
63. C2×#41D43semidirect
70. #41C2×D43semidirect
71. #41C2×D43semidirect
74. C2×Q8C2×D43semidirect
78. C2×D4C2×D43semidirect
80. C22×C4C2×D43semidirect

Maximal subgroups

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

subgroupindex
#130633732
#130633722
#130633712
#130633702
C2×#106218982
#41×D432
C2×#41×C432
#58543