Finite Group Databasebeta

← #43248553

Subgroups — #43248553

Order 28352.

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#28381934C212yesmaximal, complemented
2#28381933C214yesmaximal, complemented
3#28381932C214yesmaximal, complemented
4#28381931C216yesmaximal, complemented
5C2×#20296787C216yesmaximal, complemented
6#41×D443C218yesmaximal, complemented
7C2×#41×C443C211yesmaximal, characteristic, complemented
8#20296788C2218yescomplemented
9#20296787C22112yescomplemented
10#20296787C2214yescomplemented
11#20296787C22112yescomplemented
12#20296787C22112yescomplemented
13#20296786C22124yescomplemented
14C2×Dic886C2216yescomplemented
15Q8×D443C2218yescomplemented
16C2×D1772C2216yescomplemented
17C2×C22⋊D443C22112yescomplemented
18D4×D443C22124yescomplemented
19C2×C4×D443C22112yescomplemented
20#41×C443C2214yescomplemented
21#41×C443C2214yescomplemented
22C2×Q8×C443C2211yescharacteristic, complemented
23C2×D4×C443C2213yescomplemented
24C22×C4×C443C2213yescomplemented
25C22×D443C23112yes—
26Dic886C23112yes—
27Dic886C2314yes—
28D1772C23112yes—
29D1772C2314yes—
30C22⋊D443C23124yes—
31C22⋊D443C2318yes—
32C2×Dic443C23112yes—
33C4×D443C2318yes—
34C4×D443C23124yes—
35C23×C443C2313yes—
36Q8×C443C2314yes—
37D4×C443C23112yes—
38C2×C4×C443C2311yescharacteristic
39C2×C4×C443C2313yes—
40C2×C4×C443C2316yes—
41C2×C4×C443C2316yes—
42C22×C443—43no—
43C22×C443C2411yescharacteristic
44C22×C443C2416yes—
45C2×D443—412no—
46C2×D443C2418yes—
47C4×C443C2411yescharacteristic
48C4×C443C2416yes—
49C4×C443C2411yescharacteristic
50Dic443C2418yes—
51C2×C443—26no—
52C2×C443—21no—
53C2×C443C2511yescharacteristic
54D443—28no—
55C443#58511yescharacteristic, complemented, Sylow
56#585—4431nomaximal, Sylow
572−1+4—4434no—
582−1+4—4432no—
59H(5,𝔽2)—4434no—
60H(5,𝔽2)—4436no—
61C2×#41—4438no—
62C2×#41—4436no—
63C2×#41D44311yescharacteristic, complemented
64#41—4438no—
65#41—44324no—
66#41—44312no—
67#41—4434no—
68#41—44312no—
69#41—44312no—
70#41C2×D44314yescomplemented
71#41C2×D44314yescomplemented
72C2×Q8—4438no—
73C2×Q8—4436no—
74C2×Q8C2×D44311yescharacteristic, complemented
75C2×D4—44312no—
76C2×D4—44324no—
77C2×D4—4436no—
78C2×D4C2×D44313yescomplemented
79C22×C4—44312no—
80C22×C4C2×D44313yescomplemented
81C23—44312no—
82C23C22×D44313yes—
83Q8—44312no—
84Q8—4434no—
85Q8C22×D44314yes—
86D4—44324no—
87D4—4438no—
88D4—44312no—
89D4—4434no—
90D4C22×D443112yes—
91C2×C4—44312no—
92C2×C4—44324no—
93C2×C4—4438no—
94C2×C4C22×D44316yes—
95C2×C4C22×D44313yes—
96C2×C4C22×D44316yes—
97C2×C4C22×D44311yescharacteristic
98C22—43no—
99C22—4438no—
100C22—177212no—
101C22C23×D44316yes—
102C22C23×D44311yescharacteristic
103C4—4438no—
104C4C23×D44316yes—
105C4C23×D44311yescharacteristic
106C4C23×D44311yescharacteristic
107C2—21no—
108C2—26no—
109C2—8868no—
110C2C24×D44311yescharacteristic
subgroupG/H
centerC4C23×D443
commutator, socle, cosocleC2×C443C25
FrattiniC2C24×D443
FittingC2×#41×C443C2
hypercenterC2×#41D443
hypocenterC443#585
LCSG ▷ C2×C443 ▷ C443
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #28381934C2semidirect
2. #28381933C2semidirect
3. #28381932C2semidirect
4. #28381931C2semidirect
5. C2×#20296787C2semidirect
6. #41×D443C2semidirect
7. C2×#41×C443C2semidirect
8. #20296788C22semidirect
9. #20296787C22semidirect
10. #20296787C22semidirect
11. #20296787C22semidirect
12. #20296787C22semidirect
13. #20296786C22semidirect
14. C2×Dic886C22semidirect
15. Q8×D443C22semidirect
16. C2×D1772C22semidirect
17. C2×C22⋊D443C22semidirect
18. D4×D443C22semidirect
19. C2×C4×D443C22semidirect
20. #41×C443C22semidirect
21. #41×C443C22semidirect
22. C2×Q8×C443C22semidirect
23. C2×D4×C443C22semidirect
24. C22×C4×C443C22semidirect
55. C443#585semidirect
63. C2×#41D443semidirect
70. #41C2×D443semidirect
71. #41C2×D443semidirect
74. C2×Q8C2×D443semidirect
78. C2×D4C2×D443semidirect
80. C22×C4C2×D443semidirect

Maximal subgroups

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

subgroupindex
#283819342
#283819332
#283819322
#283819312
C2×#202967872
#41×D4432
C2×#41×C4432
#585443