Finite Group Databasebeta

← #38786950

Subgroups — #38786950

Order 25664.

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#27165785C212yesmaximal, complemented
2#27165784C214yesmaximal, complemented
3#27165783C214yesmaximal, complemented
4#27165782C216yesmaximal, complemented
5C2×#20264366C216yesmaximal, complemented
6#41×D401C218yesmaximal, complemented
7C2×#41×C401C211yesmaximal, characteristic, complemented
8#20264367C2218yescomplemented
9#20264366C22112yescomplemented
10#20264366C2214yescomplemented
11#20264366C22112yescomplemented
12#20264366C22112yescomplemented
13#20264365C22124yescomplemented
14C2×Dic802C2216yescomplemented
15Q8×D401C2218yescomplemented
16C2×D1604C2216yescomplemented
17C2×C22⋊D401C22112yescomplemented
18D4×D401C22124yescomplemented
19C2×C4×D401C22112yescomplemented
20#41×C401C2214yescomplemented
21#41×C401C2214yescomplemented
22C2×Q8×C401C2211yescharacteristic, complemented
23C2×D4×C401C2213yescomplemented
24C22×C4×C401C2213yescomplemented
25C22×D401C23112yes—
26Dic802C23112yes—
27Dic802C2314yes—
28D1604C23112yes—
29D1604C2314yes—
30C22⋊D401C23124yes—
31C22⋊D401C2318yes—
32C2×Dic401C23112yes—
33C4×D401C2318yes—
34C4×D401C23124yes—
35C23×C401C2313yes—
36Q8×C401C2314yes—
37D4×C401C23112yes—
38C2×C4×C401C2311yescharacteristic
39C2×C4×C401C2313yes—
40C2×C4×C401C2316yes—
41C2×C4×C401C2316yes—
42C22×C401—43no—
43C22×C401C2411yescharacteristic
44C22×C401C2416yes—
45C2×D401—412no—
46C2×D401C2418yes—
47C4×C401C2411yescharacteristic
48C4×C401C2416yes—
49C4×C401C2411yescharacteristic
50Dic401C2418yes—
51C2×C401—26no—
52C2×C401—21no—
53C2×C401C2511yescharacteristic
54D401—28no—
55C401#58511yescharacteristic, complemented, Sylow
56#585—4011nomaximal, Sylow
572−1+4—4014no—
582−1+4—4012no—
59H(5,𝔽2)—4014no—
60H(5,𝔽2)—4016no—
61C2×#41—4018no—
62C2×#41—4016no—
63C2×#41D40111yescharacteristic, complemented
64#41—4018no—
65#41—40124no—
66#41—40112no—
67#41—4014no—
68#41—40112no—
69#41—40112no—
70#41C2×D40114yescomplemented
71#41C2×D40114yescomplemented
72C2×Q8—4018no—
73C2×Q8—4016no—
74C2×Q8C2×D40111yescharacteristic, complemented
75C2×D4—40112no—
76C2×D4—40124no—
77C2×D4—4016no—
78C2×D4C2×D40113yescomplemented
79C22×C4—40112no—
80C22×C4C2×D40113yescomplemented
81C23—40112no—
82C23C22×D40113yes—
83Q8—40112no—
84Q8—4014no—
85Q8C22×D40114yes—
86D4—40124no—
87D4—4018no—
88D4—40112no—
89D4—4014no—
90D4C22×D401112yes—
91C2×C4—40112no—
92C2×C4—40124no—
93C2×C4—4018no—
94C2×C4C22×D40116yes—
95C2×C4C22×D40113yes—
96C2×C4C22×D40116yes—
97C2×C4C22×D40111yescharacteristic
98C22—43no—
99C22—160412no—
100C22—4018no—
101C22C23×D40116yes—
102C22C23×D40111yescharacteristic
103C4—4018no—
104C4C23×D40116yes—
105C4C23×D40111yescharacteristic
106C4C23×D40111yescharacteristic
107C2—21no—
108C2—26no—
109C2—8028no—
110C2C24×D40111yescharacteristic
subgroupG/H
centerC4C23×D401
commutator, socle, cosocleC2×C401C25
FrattiniC2C24×D401
FittingC2×#41×C401C2
hypercenterC2×#41D401
hypocenterC401#585
LCSG ▷ C2×C401 ▷ C401
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #27165785C2semidirect
2. #27165784C2semidirect
3. #27165783C2semidirect
4. #27165782C2semidirect
5. C2×#20264366C2semidirect
6. #41×D401C2semidirect
7. C2×#41×C401C2semidirect
8. #20264367C22semidirect
9. #20264366C22semidirect
10. #20264366C22semidirect
11. #20264366C22semidirect
12. #20264366C22semidirect
13. #20264365C22semidirect
14. C2×Dic802C22semidirect
15. Q8×D401C22semidirect
16. C2×D1604C22semidirect
17. C2×C22⋊D401C22semidirect
18. D4×D401C22semidirect
19. C2×C4×D401C22semidirect
20. #41×C401C22semidirect
21. #41×C401C22semidirect
22. C2×Q8×C401C22semidirect
23. C2×D4×C401C22semidirect
24. C22×C4×C401C22semidirect
55. C401#585semidirect
63. C2×#41D401semidirect
70. #41C2×D401semidirect
71. #41C2×D401semidirect
74. C2×Q8C2×D401semidirect
78. C2×D4C2×D401semidirect
80. C22×C4C2×D401semidirect

Maximal subgroups

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

subgroupindex
#271657852
#271657842
#271657832
#271657822
C2×#202643662
#41×D4012
C2×#41×C4012
#585401