Finite Group Databasebeta

← #44501231

Subgroups — #44501231

Order 30656.

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#29506430C212yesmaximal, complemented
2#29506429C214yesmaximal, complemented
3#29506428C214yesmaximal, complemented
4#29506427C216yesmaximal, complemented
5C2×#21440162C216yesmaximal, complemented
6#41×D479C218yesmaximal, complemented
7C2×#41×C479C211yesmaximal, characteristic, complemented
8#21440163C2218yescomplemented
9#21440162C22112yescomplemented
10#21440162C2214yescomplemented
11#21440162C22112yescomplemented
12#21440162C22112yescomplemented
13#21440161C22124yescomplemented
14C2×Dic958C2216yescomplemented
15Q8×D479C2218yescomplemented
16C2×D1916C2216yescomplemented
17C2×C22⋊D479C22112yescomplemented
18D4×D479C22124yescomplemented
19C2×C4×D479C22112yescomplemented
20#41×C479C2214yescomplemented
21#41×C479C2214yescomplemented
22C2×Q8×C479C2211yescharacteristic, complemented
23C2×D4×C479C2213yescomplemented
24C22×C4×C479C2213yescomplemented
25C22×D479C23112yes—
26Dic958C23112yes—
27Dic958C2314yes—
28D1916C23112yes—
29D1916C2314yes—
30C22⋊D479C23124yes—
31C22⋊D479C2318yes—
32C2×Dic479C23112yes—
33C4×D479C2318yes—
34C4×D479C23124yes—
35C23×C479C2313yes—
36Q8×C479C2314yes—
37D4×C479C23112yes—
38C2×C4×C479C2311yescharacteristic
39C2×C4×C479C2313yes—
40C2×C4×C479C2316yes—
41C2×C4×C479C2316yes—
42C22×C479—43no—
43C22×C479C2411yescharacteristic
44C22×C479C2416yes—
45C2×D479—412no—
46C2×D479C2418yes—
47C4×C479C2411yescharacteristic
48C4×C479C2416yes—
49C4×C479C2411yescharacteristic
50Dic479C2418yes—
51C2×C479—26no—
52C2×C479—21no—
53C2×C479C2511yescharacteristic
54D479—28no—
55C479#58511yescharacteristic, complemented, Sylow
56#585—4791nomaximal, Sylow
572−1+4—4794no—
582−1+4—4792no—
59H(5,𝔽2)—4794no—
60H(5,𝔽2)—4796no—
61C2×#41—4798no—
62C2×#41—4796no—
63C2×#41D47911yescharacteristic, complemented
64#41—4798no—
65#41—47924no—
66#41—47912no—
67#41—4794no—
68#41—47912no—
69#41—47912no—
70#41C2×D47914yescomplemented
71#41C2×D47914yescomplemented
72C2×Q8—4798no—
73C2×Q8—4796no—
74C2×Q8C2×D47911yescharacteristic, complemented
75C2×D4—47912no—
76C2×D4—47924no—
77C2×D4—4796no—
78C2×D4C2×D47913yescomplemented
79C22×C4—47912no—
80C22×C4C2×D47913yescomplemented
81C23—47912no—
82C23C22×D47913yes—
83Q8—47912no—
84Q8—4794no—
85Q8C22×D47914yes—
86D4—47924no—
87D4—4798no—
88D4—47912no—
89D4—4794no—
90D4C22×D479112yes—
91C2×C4—47912no—
92C2×C4—47924no—
93C2×C4—4798no—
94C2×C4C22×D47916yes—
95C2×C4C22×D47913yes—
96C2×C4C22×D47916yes—
97C2×C4C22×D47911yescharacteristic
98C22—43no—
99C22—191612no—
100C22—4798no—
101C22C23×D47916yes—
102C22C23×D47911yescharacteristic
103C4—4798no—
104C4C23×D47916yes—
105C4C23×D47911yescharacteristic
106C4C23×D47911yescharacteristic
107C2—21no—
108C2—26no—
109C2—9588no—
110C2C24×D47911yescharacteristic
subgroupG/H
centerC4C23×D479
commutator, socle, cosocleC2×C479C25
FrattiniC2C24×D479
FittingC2×#41×C479C2
hypercenterC2×#41D479
hypocenterC479#585
LCSG ▷ C2×C479 ▷ C479
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #29506430C2semidirect
2. #29506429C2semidirect
3. #29506428C2semidirect
4. #29506427C2semidirect
5. C2×#21440162C2semidirect
6. #41×D479C2semidirect
7. C2×#41×C479C2semidirect
8. #21440163C22semidirect
9. #21440162C22semidirect
10. #21440162C22semidirect
11. #21440162C22semidirect
12. #21440162C22semidirect
13. #21440161C22semidirect
14. C2×Dic958C22semidirect
15. Q8×D479C22semidirect
16. C2×D1916C22semidirect
17. C2×C22⋊D479C22semidirect
18. D4×D479C22semidirect
19. C2×C4×D479C22semidirect
20. #41×C479C22semidirect
21. #41×C479C22semidirect
22. C2×Q8×C479C22semidirect
23. C2×D4×C479C22semidirect
24. C22×C4×C479C22semidirect
55. C479#585semidirect
63. C2×#41D479semidirect
70. #41C2×D479semidirect
71. #41C2×D479semidirect
74. C2×Q8C2×D479semidirect
78. C2×D4C2×D479semidirect
80. C22×C4C2×D479semidirect

Maximal subgroups

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

subgroupindex
#295064302
#295064292
#295064282
#295064272
C2×#214401622
#41×D4792
C2×#41×C4792
#585479