Finite Group Databasebeta

← #43244440

Subgroups — #43244440

Order 28096.

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#28380791C212yesmaximal, complemented
2#28380790C214yesmaximal, complemented
3#28380789C214yesmaximal, complemented
4#28380788C216yesmaximal, complemented
5C2×#20296329C216yesmaximal, complemented
6#41×D439C218yesmaximal, complemented
7C2×#41×C439C211yesmaximal, characteristic, complemented
8#20296330C2218yescomplemented
9#20296329C22112yescomplemented
10#20296329C2214yescomplemented
11#20296329C22112yescomplemented
12#20296329C22112yescomplemented
13#20296328C22124yescomplemented
14C2×Dic878C2216yescomplemented
15Q8×D439C2218yescomplemented
16C2×D1756C2216yescomplemented
17C2×C22⋊D439C22112yescomplemented
18D4×D439C22124yescomplemented
19C2×C4×D439C22112yescomplemented
20#41×C439C2214yescomplemented
21#41×C439C2214yescomplemented
22C2×Q8×C439C2211yescharacteristic, complemented
23C2×D4×C439C2213yescomplemented
24C22×C4×C439C2213yescomplemented
25C22×D439C23112yes—
26Dic878C23112yes—
27Dic878C2314yes—
28D1756C23112yes—
29D1756C2314yes—
30C22⋊D439C23124yes—
31C22⋊D439C2318yes—
32C2×Dic439C23112yes—
33C4×D439C2318yes—
34C4×D439C23124yes—
35C23×C439C2313yes—
36Q8×C439C2314yes—
37D4×C439C23112yes—
38C2×C4×C439C2311yescharacteristic
39C2×C4×C439C2313yes—
40C2×C4×C439C2316yes—
41C2×C4×C439C2316yes—
42C22×C439—43no—
43C22×C439C2411yescharacteristic
44C22×C439C2416yes—
45C2×D439—412no—
46C2×D439C2418yes—
47C4×C439C2411yescharacteristic
48C4×C439C2416yes—
49C4×C439C2411yescharacteristic
50Dic439C2418yes—
51C2×C439—26no—
52C2×C439—21no—
53C2×C439C2511yescharacteristic
54D439—28no—
55C439#58511yescharacteristic, complemented, Sylow
56#585—4391nomaximal, Sylow
572−1+4—4394no—
582−1+4—4392no—
59H(5,𝔽2)—4394no—
60H(5,𝔽2)—4396no—
61C2×#41—4398no—
62C2×#41—4396no—
63C2×#41D43911yescharacteristic, complemented
64#41—4398no—
65#41—43924no—
66#41—43912no—
67#41—4394no—
68#41—43912no—
69#41—43912no—
70#41C2×D43914yescomplemented
71#41C2×D43914yescomplemented
72C2×Q8—4398no—
73C2×Q8—4396no—
74C2×Q8C2×D43911yescharacteristic, complemented
75C2×D4—43912no—
76C2×D4—43924no—
77C2×D4—4396no—
78C2×D4C2×D43913yescomplemented
79C22×C4—43912no—
80C22×C4C2×D43913yescomplemented
81C23—43912no—
82C23C22×D43913yes—
83Q8—43912no—
84Q8—4394no—
85Q8C22×D43914yes—
86D4—43924no—
87D4—4398no—
88D4—43912no—
89D4—4394no—
90D4C22×D439112yes—
91C2×C4—43912no—
92C2×C4—43924no—
93C2×C4—4398no—
94C2×C4C22×D43916yes—
95C2×C4C22×D43913yes—
96C2×C4C22×D43916yes—
97C2×C4C22×D43911yescharacteristic
98C22—43no—
99C22—4398no—
100C22—175612no—
101C22C23×D43916yes—
102C22C23×D43911yescharacteristic
103C4—4398no—
104C4C23×D43916yes—
105C4C23×D43911yescharacteristic
106C4C23×D43911yescharacteristic
107C2—21no—
108C2—26no—
109C2—8788no—
110C2C24×D43911yescharacteristic
subgroupG/H
centerC4C23×D439
commutator, socle, cosocleC2×C439C25
FrattiniC2C24×D439
FittingC2×#41×C439C2
hypercenterC2×#41D439
hypocenterC439#585
LCSG ▷ C2×C439 ▷ C439
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #28380791C2semidirect
2. #28380790C2semidirect
3. #28380789C2semidirect
4. #28380788C2semidirect
5. C2×#20296329C2semidirect
6. #41×D439C2semidirect
7. C2×#41×C439C2semidirect
8. #20296330C22semidirect
9. #20296329C22semidirect
10. #20296329C22semidirect
11. #20296329C22semidirect
12. #20296329C22semidirect
13. #20296328C22semidirect
14. C2×Dic878C22semidirect
15. Q8×D439C22semidirect
16. C2×D1756C22semidirect
17. C2×C22⋊D439C22semidirect
18. D4×D439C22semidirect
19. C2×C4×D439C22semidirect
20. #41×C439C22semidirect
21. #41×C439C22semidirect
22. C2×Q8×C439C22semidirect
23. C2×D4×C439C22semidirect
24. C22×C4×C439C22semidirect
55. C439#585semidirect
63. C2×#41D439semidirect
70. #41C2×D439semidirect
71. #41C2×D439semidirect
74. C2×Q8C2×D439semidirect
78. C2×D4C2×D439semidirect
80. C22×C4C2×D439semidirect

Maximal subgroups

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

subgroupindex
#283807912
#283807902
#283807892
#283807882
C2×#202963292
#41×D4392
C2×#41×C4392
#585439