Finite Group Databasebeta

← #39910083

Subgroups — #39910083

Order 26176.

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#27189765C212yesmaximal, complemented
2#27189764C214yesmaximal, complemented
3#27189763C214yesmaximal, complemented
4#27189762C216yesmaximal, complemented
5C2×#20266988C216yesmaximal, complemented
6#41×D409C218yesmaximal, complemented
7C2×#41×C409C211yesmaximal, characteristic, complemented
8#20266989C2218yescomplemented
9#20266988C2214yescomplemented
10#20266988C22112yescomplemented
11#20266988C22112yescomplemented
12#20266988C22112yescomplemented
13#20266987C22124yescomplemented
14C2×Dic818C2216yescomplemented
15Q8×D409C2218yescomplemented
16C2×D1636C2216yescomplemented
17C2×C22⋊D409C22112yescomplemented
18D4×D409C22124yescomplemented
19C2×C4×D409C22112yescomplemented
20#41×C409C2214yescomplemented
21#41×C409C2214yescomplemented
22C2×Q8×C409C2211yescharacteristic, complemented
23C2×D4×C409C2213yescomplemented
24C22×C4×C409C2213yescomplemented
25C22×D409C23112yes—
26Dic818C23112yes—
27Dic818C2314yes—
28D1636C23112yes—
29D1636C2314yes—
30C22⋊D409C23124yes—
31C22⋊D409C2318yes—
32C2×Dic409C23112yes—
33C4×D409C2318yes—
34C4×D409C23124yes—
35C23×C409C2313yes—
36Q8×C409C2314yes—
37D4×C409C23112yes—
38C2×C4×C409C2311yescharacteristic
39C2×C4×C409C2313yes—
40C2×C4×C409C2316yes—
41C2×C4×C409C2316yes—
42C22×C409—43no—
43C22×C409C2416yes—
44C22×C409C2411yescharacteristic
45C2×D409—412no—
46C2×D409C2418yes—
47C4×C409C2416yes—
48C4×C409C2411yescharacteristic
49C4×C409C2411yescharacteristic
50Dic409C2418yes—
51C2×C409—26no—
52C2×C409—21no—
53C2×C409C2511yescharacteristic
54D409—28no—
55C409#58511yescharacteristic, complemented, Sylow
56#585—4091nomaximal, Sylow
572−1+4—4094no—
582−1+4—4092no—
59H(5,𝔽2)—4094no—
60H(5,𝔽2)—4096no—
61C2×#41—4098no—
62C2×#41—4096no—
63C2×#41D40911yescharacteristic, complemented
64#41—4098no—
65#41—40924no—
66#41—40912no—
67#41—4094no—
68#41—40912no—
69#41—40912no—
70#41C2×D40914yescomplemented
71#41C2×D40914yescomplemented
72C2×Q8—4098no—
73C2×Q8—4096no—
74C2×Q8C2×D40911yescharacteristic, complemented
75C2×D4—40912no—
76C2×D4—40924no—
77C2×D4—4096no—
78C2×D4C2×D40913yescomplemented
79C22×C4—40912no—
80C22×C4C2×D40913yescomplemented
81C23—40912no—
82C23C22×D40913yes—
83Q8—40912no—
84Q8—4094no—
85Q8C22×D40914yes—
86D4—40924no—
87D4—4098no—
88D4—40912no—
89D4—4094no—
90D4C22×D409112yes—
91C2×C4—40912no—
92C2×C4—40924no—
93C2×C4—4098no—
94C2×C4C22×D40916yes—
95C2×C4C22×D40913yes—
96C2×C4C22×D40916yes—
97C2×C4C22×D40911yescharacteristic
98C22—43no—
99C22—163612no—
100C22—4098no—
101C22C23×D40916yes—
102C22C23×D40911yescharacteristic
103C4—4098no—
104C4C23×D40916yes—
105C4C23×D40911yescharacteristic
106C4C23×D40911yescharacteristic
107C2—21no—
108C2—26no—
109C2—8188no—
110C2C24×D40911yescharacteristic
subgroupG/H
centerC4C23×D409
commutator, socle, cosocleC2×C409C25
FrattiniC2C24×D409
FittingC2×#41×C409C2
hypercenterC2×#41D409
hypocenterC409#585
LCSG ▷ C2×C409 ▷ C409
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #27189765C2semidirect
2. #27189764C2semidirect
3. #27189763C2semidirect
4. #27189762C2semidirect
5. C2×#20266988C2semidirect
6. #41×D409C2semidirect
7. C2×#41×C409C2semidirect
8. #20266989C22semidirect
9. #20266988C22semidirect
10. #20266988C22semidirect
11. #20266988C22semidirect
12. #20266988C22semidirect
13. #20266987C22semidirect
14. C2×Dic818C22semidirect
15. Q8×D409C22semidirect
16. C2×D1636C22semidirect
17. C2×C22⋊D409C22semidirect
18. D4×D409C22semidirect
19. C2×C4×D409C22semidirect
20. #41×C409C22semidirect
21. #41×C409C22semidirect
22. C2×Q8×C409C22semidirect
23. C2×D4×C409C22semidirect
24. C22×C4×C409C22semidirect
55. C409#585semidirect
63. C2×#41D409semidirect
70. #41C2×D409semidirect
71. #41C2×D409semidirect
74. C2×Q8C2×D409semidirect
78. C2×D4C2×D409semidirect
80. C22×C4C2×D409semidirect

Maximal subgroups

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

subgroupindex
#271897652
#271897642
#271897632
#271897622
C2×#202669882
#41×D4092
C2×#41×C4092
#585409