Finite Group Databasebeta

← #38734935

Subgroups — #38734935

Order 24896.

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#27159432C212yesmaximal, complemented
2#27159431C214yesmaximal, complemented
3#27159430C214yesmaximal, complemented
4#27159429C216yesmaximal, complemented
5C2×#20261966C216yesmaximal, complemented
6#41×D389C218yesmaximal, complemented
7C2×#41×C389C211yesmaximal, characteristic, complemented
8#20261967C2218yescomplemented
9#20261966C22112yescomplemented
10#20261966C2214yescomplemented
11#20261966C22112yescomplemented
12#20261966C22112yescomplemented
13#20261965C22124yescomplemented
14C2×Dic778C2216yescomplemented
15Q8×D389C2218yescomplemented
16C2×D1556C2216yescomplemented
17C2×C22⋊D389C22112yescomplemented
18D4×D389C22124yescomplemented
19C2×C4×D389C22112yescomplemented
20#41×C389C2214yescomplemented
21#41×C389C2214yescomplemented
22C2×Q8×C389C2211yescharacteristic, complemented
23C2×D4×C389C2213yescomplemented
24C22×C4×C389C2213yescomplemented
25C22×D389C23112yes—
26Dic778C23112yes—
27Dic778C2314yes—
28D1556C23112yes—
29D1556C2314yes—
30C22⋊D389C23124yes—
31C22⋊D389C2318yes—
32C2×Dic389C23112yes—
33C4×D389C2318yes—
34C4×D389C23124yes—
35C23×C389C2313yes—
36Q8×C389C2314yes—
37D4×C389C23112yes—
38C2×C4×C389C2311yescharacteristic
39C2×C4×C389C2313yes—
40C2×C4×C389C2316yes—
41C2×C4×C389C2316yes—
42C22×C389—43no—
43C22×C389C2411yescharacteristic
44C22×C389C2416yes—
45C2×D389—412no—
46C2×D389C2418yes—
47C4×C389C2411yescharacteristic
48C4×C389C2416yes—
49C4×C389C2411yescharacteristic
50Dic389C2418yes—
51C2×C389—26no—
52C2×C389—21no—
53C2×C389C2511yescharacteristic
54D389—28no—
55C389#58511yescharacteristic, complemented, Sylow
56#585—3891nomaximal, Sylow
572−1+4—3894no—
582−1+4—3892no—
59H(5,𝔽2)—3894no—
60H(5,𝔽2)—3896no—
61C2×#41—3898no—
62C2×#41—3896no—
63C2×#41D38911yescharacteristic, complemented
64#41—3898no—
65#41—38924no—
66#41—38912no—
67#41—3894no—
68#41—38912no—
69#41—38912no—
70#41C2×D38914yescomplemented
71#41C2×D38914yescomplemented
72C2×Q8—3898no—
73C2×Q8—3896no—
74C2×Q8C2×D38911yescharacteristic, complemented
75C2×D4—38912no—
76C2×D4—38924no—
77C2×D4—3896no—
78C2×D4C2×D38913yescomplemented
79C22×C4—38912no—
80C22×C4C2×D38913yescomplemented
81C23—38912no—
82C23C22×D38913yes—
83Q8—38912no—
84Q8—3894no—
85Q8C22×D38914yes—
86D4—38924no—
87D4—3898no—
88D4—38912no—
89D4—3894no—
90D4C22×D389112yes—
91C2×C4—38912no—
92C2×C4—38924no—
93C2×C4—3898no—
94C2×C4C22×D38916yes—
95C2×C4C22×D38913yes—
96C2×C4C22×D38916yes—
97C2×C4C22×D38911yescharacteristic
98C22—43no—
99C22—155612no—
100C22—3898no—
101C22C23×D38916yes—
102C22C23×D38911yescharacteristic
103C4—3898no—
104C4C23×D38916yes—
105C4C23×D38911yescharacteristic
106C4C23×D38911yescharacteristic
107C2—21no—
108C2—26no—
109C2—7788no—
110C2C24×D38911yescharacteristic
subgroupG/H
centerC4C23×D389
commutator, socle, cosocleC2×C389C25
FrattiniC2C24×D389
FittingC2×#41×C389C2
hypercenterC2×#41D389
hypocenterC389#585
LCSG ▷ C2×C389 ▷ C389
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #27159432C2semidirect
2. #27159431C2semidirect
3. #27159430C2semidirect
4. #27159429C2semidirect
5. C2×#20261966C2semidirect
6. #41×D389C2semidirect
7. C2×#41×C389C2semidirect
8. #20261967C22semidirect
9. #20261966C22semidirect
10. #20261966C22semidirect
11. #20261966C22semidirect
12. #20261966C22semidirect
13. #20261965C22semidirect
14. C2×Dic778C22semidirect
15. Q8×D389C22semidirect
16. C2×D1556C22semidirect
17. C2×C22⋊D389C22semidirect
18. D4×D389C22semidirect
19. C2×C4×D389C22semidirect
20. #41×C389C22semidirect
21. #41×C389C22semidirect
22. C2×Q8×C389C22semidirect
23. C2×D4×C389C22semidirect
24. C22×C4×C389C22semidirect
55. C389#585semidirect
63. C2×#41D389semidirect
70. #41C2×D389semidirect
71. #41C2×D389semidirect
74. C2×Q8C2×D389semidirect
78. C2×D4C2×D389semidirect
80. C22×C4C2×D389semidirect

Maximal subgroups

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

subgroupindex
#271594322
#271594312
#271594302
#271594292
C2×#202619662
#41×D3892
C2×#41×C3892
#585389