Finite Group Databasebeta

← #38763358

Subgroups — #38763358

Order 25408.

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#27163144C212yesmaximal, complemented
2#27163143C214yesmaximal, complemented
3#27163142C214yesmaximal, complemented
4#27163141C216yesmaximal, complemented
5C2×#20263731C216yesmaximal, complemented
6#41×D397C218yesmaximal, complemented
7C2×#41×C397C211yesmaximal, characteristic, complemented
8#20263732C2218yescomplemented
9#20263731C22112yescomplemented
10#20263731C2214yescomplemented
11#20263731C22112yescomplemented
12#20263731C22112yescomplemented
13#20263730C22124yescomplemented
14C2×Dic794C2216yescomplemented
15Q8×D397C2218yescomplemented
16C2×D1588C2216yescomplemented
17C2×C22⋊D397C22112yescomplemented
18D4×D397C22124yescomplemented
19C2×C4×D397C22112yescomplemented
20#41×C397C2214yescomplemented
21#41×C397C2214yescomplemented
22C2×Q8×C397C2211yescharacteristic, complemented
23C2×D4×C397C2213yescomplemented
24C22×C4×C397C2213yescomplemented
25C22×D397C23112yes—
26Dic794C23112yes—
27Dic794C2314yes—
28D1588C23112yes—
29D1588C2314yes—
30C22⋊D397C23124yes—
31C22⋊D397C2318yes—
32C2×Dic397C23112yes—
33C4×D397C2318yes—
34C4×D397C23124yes—
35C23×C397C2313yes—
36Q8×C397C2314yes—
37D4×C397C23112yes—
38C2×C4×C397C2311yescharacteristic
39C2×C4×C397C2313yes—
40C2×C4×C397C2316yes—
41C2×C4×C397C2316yes—
42C22×C397—43no—
43C22×C397C2411yescharacteristic
44C22×C397C2416yes—
45C2×D397—412no—
46C2×D397C2418yes—
47C4×C397C2411yescharacteristic
48C4×C397C2416yes—
49C4×C397C2411yescharacteristic
50Dic397C2418yes—
51C2×C397—26no—
52C2×C397—21no—
53C2×C397C2511yescharacteristic
54D397—28no—
55C397#58511yescharacteristic, complemented, Sylow
56#585—3971nomaximal, Sylow
572−1+4—3974no—
582−1+4—3972no—
59H(5,𝔽2)—3974no—
60H(5,𝔽2)—3976no—
61C2×#41—3978no—
62C2×#41—3976no—
63C2×#41D39711yescharacteristic, complemented
64#41—3978no—
65#41—39724no—
66#41—39712no—
67#41—3974no—
68#41—39712no—
69#41—39712no—
70#41C2×D39714yescomplemented
71#41C2×D39714yescomplemented
72C2×Q8—3978no—
73C2×Q8—3976no—
74C2×Q8C2×D39711yescharacteristic, complemented
75C2×D4—39712no—
76C2×D4—39724no—
77C2×D4—3976no—
78C2×D4C2×D39713yescomplemented
79C22×C4—39712no—
80C22×C4C2×D39713yescomplemented
81C23—39712no—
82C23C22×D39713yes—
83Q8—39712no—
84Q8—3974no—
85Q8C22×D39714yes—
86D4—39724no—
87D4—3978no—
88D4—39712no—
89D4—3974no—
90D4C22×D397112yes—
91C2×C4—39712no—
92C2×C4—39724no—
93C2×C4—3978no—
94C2×C4C22×D39716yes—
95C2×C4C22×D39713yes—
96C2×C4C22×D39716yes—
97C2×C4C22×D39711yescharacteristic
98C22—43no—
99C22—158812no—
100C22—3978no—
101C22C23×D39716yes—
102C22C23×D39711yescharacteristic
103C4—3978no—
104C4C23×D39716yes—
105C4C23×D39711yescharacteristic
106C4C23×D39711yescharacteristic
107C2—21no—
108C2—26no—
109C2—7948no—
110C2C24×D39711yescharacteristic
subgroupG/H
centerC4C23×D397
commutator, socle, cosocleC2×C397C25
FrattiniC2C24×D397
FittingC2×#41×C397C2
hypercenterC2×#41D397
hypocenterC397#585
LCSG ▷ C2×C397 ▷ C397
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #27163144C2semidirect
2. #27163143C2semidirect
3. #27163142C2semidirect
4. #27163141C2semidirect
5. C2×#20263731C2semidirect
6. #41×D397C2semidirect
7. C2×#41×C397C2semidirect
8. #20263732C22semidirect
9. #20263731C22semidirect
10. #20263731C22semidirect
11. #20263731C22semidirect
12. #20263731C22semidirect
13. #20263730C22semidirect
14. C2×Dic794C22semidirect
15. Q8×D397C22semidirect
16. C2×D1588C22semidirect
17. C2×C22⋊D397C22semidirect
18. D4×D397C22semidirect
19. C2×C4×D397C22semidirect
20. #41×C397C22semidirect
21. #41×C397C22semidirect
22. C2×Q8×C397C22semidirect
23. C2×D4×C397C22semidirect
24. C22×C4×C397C22semidirect
55. C397#585semidirect
63. C2×#41D397semidirect
70. #41C2×D397semidirect
71. #41C2×D397semidirect
74. C2×Q8C2×D397semidirect
78. C2×D4C2×D397semidirect
80. C22×C4C2×D397semidirect

Maximal subgroups

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

subgroupindex
#271631442
#271631432
#271631422
#271631412
C2×#202637312
#41×D3972
C2×#41×C3972
#585397