Finite Group Databasebeta

← #42119895

Subgroups — #42119895

Order 27584.

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#28352237C212yesmaximal, complemented
2#28352236C214yesmaximal, complemented
3#28352235C214yesmaximal, complemented
4#28352234C216yesmaximal, complemented
5C2×#20293800C216yesmaximal, complemented
6#41×D431C218yesmaximal, complemented
7C2×#41×C431C211yesmaximal, characteristic, complemented
8#20293801C2218yescomplemented
9#20293800C22112yescomplemented
10#20293800C2214yescomplemented
11#20293800C22112yescomplemented
12#20293800C22112yescomplemented
13#20293799C22124yescomplemented
14C2×Dic862C2216yescomplemented
15Q8×D431C2218yescomplemented
16C2×D1724C2216yescomplemented
17C2×C22⋊D431C22112yescomplemented
18D4×D431C22124yescomplemented
19C2×C4×D431C22112yescomplemented
20#41×C431C2214yescomplemented
21#41×C431C2214yescomplemented
22C2×Q8×C431C2211yescharacteristic, complemented
23C2×D4×C431C2213yescomplemented
24C22×C4×C431C2213yescomplemented
25C22×D431C23112yes—
26Dic862C23112yes—
27Dic862C2314yes—
28D1724C23112yes—
29D1724C2314yes—
30C22⋊D431C23124yes—
31C22⋊D431C2318yes—
32C2×Dic431C23112yes—
33C4×D431C2318yes—
34C4×D431C23124yes—
35C23×C431C2313yes—
36Q8×C431C2314yes—
37D4×C431C23112yes—
38C2×C4×C431C2311yescharacteristic
39C2×C4×C431C2313yes—
40C2×C4×C431C2316yes—
41C2×C4×C431C2316yes—
42C22×C431—43no—
43C22×C431C2411yescharacteristic
44C22×C431C2416yes—
45C2×D431—412no—
46C2×D431C2418yes—
47C4×C431C2411yescharacteristic
48C4×C431C2416yes—
49C4×C431C2411yescharacteristic
50Dic431C2418yes—
51C2×C431—26no—
52C2×C431—21no—
53C2×C431C2511yescharacteristic
54D431—28no—
55C431#58511yescharacteristic, complemented, Sylow
56#585—4311nomaximal, Sylow
572−1+4—4314no—
582−1+4—4312no—
59H(5,𝔽2)—4314no—
60H(5,𝔽2)—4316no—
61C2×#41—4318no—
62C2×#41—4316no—
63C2×#41D43111yescharacteristic, complemented
64#41—4318no—
65#41—43124no—
66#41—43112no—
67#41—4314no—
68#41—43112no—
69#41—43112no—
70#41C2×D43114yescomplemented
71#41C2×D43114yescomplemented
72C2×Q8—4318no—
73C2×Q8—4316no—
74C2×Q8C2×D43111yescharacteristic, complemented
75C2×D4—43112no—
76C2×D4—43124no—
77C2×D4—4316no—
78C2×D4C2×D43113yescomplemented
79C22×C4—43112no—
80C22×C4C2×D43113yescomplemented
81C23—43112no—
82C23C22×D43113yes—
83Q8—43112no—
84Q8—4314no—
85Q8C22×D43114yes—
86D4—43124no—
87D4—4318no—
88D4—43112no—
89D4—4314no—
90D4C22×D431112yes—
91C2×C4—43112no—
92C2×C4—43124no—
93C2×C4—4318no—
94C2×C4C22×D43116yes—
95C2×C4C22×D43113yes—
96C2×C4C22×D43116yes—
97C2×C4C22×D43111yescharacteristic
98C22—43no—
99C22—4318no—
100C22—172412no—
101C22C23×D43116yes—
102C22C23×D43111yescharacteristic
103C4—4318no—
104C4C23×D43116yes—
105C4C23×D43111yescharacteristic
106C4C23×D43111yescharacteristic
107C2—21no—
108C2—26no—
109C2—8628no—
110C2C24×D43111yescharacteristic
subgroupG/H
centerC4C23×D431
commutator, socle, cosocleC2×C431C25
FrattiniC2C24×D431
FittingC2×#41×C431C2
hypercenterC2×#41D431
hypocenterC431#585
LCSG ▷ C2×C431 ▷ C431
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #28352237C2semidirect
2. #28352236C2semidirect
3. #28352235C2semidirect
4. #28352234C2semidirect
5. C2×#20293800C2semidirect
6. #41×D431C2semidirect
7. C2×#41×C431C2semidirect
8. #20293801C22semidirect
9. #20293800C22semidirect
10. #20293800C22semidirect
11. #20293800C22semidirect
12. #20293800C22semidirect
13. #20293799C22semidirect
14. C2×Dic862C22semidirect
15. Q8×D431C22semidirect
16. C2×D1724C22semidirect
17. C2×C22⋊D431C22semidirect
18. D4×D431C22semidirect
19. C2×C4×D431C22semidirect
20. #41×C431C22semidirect
21. #41×C431C22semidirect
22. C2×Q8×C431C22semidirect
23. C2×D4×C431C22semidirect
24. C22×C4×C431C22semidirect
55. C431#585semidirect
63. C2×#41D431semidirect
70. #41C2×D431semidirect
71. #41C2×D431semidirect
74. C2×Q8C2×D431semidirect
78. C2×D4C2×D431semidirect
80. C22×C4C2×D431semidirect

Maximal subgroups

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

subgroupindex
#283522372
#283522362
#283522352
#283522342
C2×#202938002
#41×D4312
C2×#41×C4312
#585431