Finite Group Databasebeta

← #45688268

Subgroups — #45688268

Order 33344.

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#30659756C212yesmaximal, complemented
2#30659755C214yesmaximal, complemented
3#30659754C214yesmaximal, complemented
4#30659753C216yesmaximal, complemented
5C2×#22552364C216yesmaximal, complemented
6#41×D521C218yesmaximal, complemented
7C2×#41×C521C211yesmaximal, characteristic, complemented
8#22552365C2218yescomplemented
9#22552364C22112yescomplemented
10#22552364C2214yescomplemented
11#22552364C22112yescomplemented
12#22552364C22112yescomplemented
13#22552363C22124yescomplemented
14C2×Dic1042C2216yescomplemented
15Q8×D521C2218yescomplemented
16C2×D2084C2216yescomplemented
17C2×C22⋊D521C22112yescomplemented
18D4×D521C22124yescomplemented
19C2×C4×D521C22112yescomplemented
20#41×C521C2214yescomplemented
21#41×C521C2214yescomplemented
22C2×Q8×C521C2211yescharacteristic, complemented
23C2×D4×C521C2213yescomplemented
24C22×C4×C521C2213yescomplemented
25C22×D521C23112yes—
26Dic1042C23112yes—
27Dic1042C2314yes—
28D2084C23112yes—
29D2084C2314yes—
30C22⋊D521C23124yes—
31C22⋊D521C2318yes—
32C2×Dic521C23112yes—
33C4×D521C2318yes—
34C4×D521C23124yes—
35C23×C521C2313yes—
36Q8×C521C2314yes—
37D4×C521C23112yes—
38C2×C4×C521C2311yescharacteristic
39C2×C4×C521C2313yes—
40C2×C4×C521C2316yes—
41C2×C4×C521C2316yes—
42C22×C521—43no—
43C22×C521C2411yescharacteristic
44C22×C521C2416yes—
45C2×D521—412no—
46C2×D521C2418yes—
47C4×C521C2411yescharacteristic
48C4×C521C2416yes—
49C4×C521C2411yescharacteristic
50Dic521C2418yes—
51C2×C521—26no—
52C2×C521—21no—
53C2×C521C2511yescharacteristic
54D521—28no—
55C521#58511yescharacteristic, complemented, Sylow
56#585—5211nomaximal, Sylow
572−1+4—5214no—
582−1+4—5212no—
59H(5,𝔽2)—5214no—
60H(5,𝔽2)—5216no—
61C2×#41—5218no—
62C2×#41—5216no—
63C2×#41D52111yescharacteristic, complemented
64#41—5218no—
65#41—52124no—
66#41—52112no—
67#41—5214no—
68#41—52112no—
69#41—52112no—
70#41C2×D52114yescomplemented
71#41C2×D52114yescomplemented
72C2×Q8—5218no—
73C2×Q8—5216no—
74C2×Q8C2×D52111yescharacteristic, complemented
75C2×D4—52112no—
76C2×D4—52124no—
77C2×D4—5216no—
78C2×D4C2×D52113yescomplemented
79C22×C4—52112no—
80C22×C4C2×D52113yescomplemented
81C23—52112no—
82C23C22×D52113yes—
83Q8—52112no—
84Q8—5214no—
85Q8C22×D52114yes—
86D4—52124no—
87D4—5218no—
88D4—52112no—
89D4—5214no—
90D4C22×D521112yes—
91C2×C4—52112no—
92C2×C4—52124no—
93C2×C4—5218no—
94C2×C4C22×D52116yes—
95C2×C4C22×D52113yes—
96C2×C4C22×D52116yes—
97C2×C4C22×D52111yescharacteristic
98C22—43no—
99C22—5218no—
100C22—208412no—
101C22C23×D52116yes—
102C22C23×D52111yescharacteristic
103C4—5218no—
104C4C23×D52116yes—
105C4C23×D52111yescharacteristic
106C4C23×D52111yescharacteristic
107C2—21no—
108C2—26no—
109C2—10428no—
110C2C24×D52111yescharacteristic
subgroupG/H
centerC4C23×D521
commutator, socle, cosocleC2×C521C25
FrattiniC2C24×D521
FittingC2×#41×C521C2
hypercenterC2×#41D521
hypocenterC521#585
LCSG ▷ C2×C521 ▷ C521
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #30659756C2semidirect
2. #30659755C2semidirect
3. #30659754C2semidirect
4. #30659753C2semidirect
5. C2×#22552364C2semidirect
6. #41×D521C2semidirect
7. C2×#41×C521C2semidirect
8. #22552365C22semidirect
9. #22552364C22semidirect
10. #22552364C22semidirect
11. #22552364C22semidirect
12. #22552364C22semidirect
13. #22552363C22semidirect
14. C2×Dic1042C22semidirect
15. Q8×D521C22semidirect
16. C2×D2084C22semidirect
17. C2×C22⋊D521C22semidirect
18. D4×D521C22semidirect
19. C2×C4×D521C22semidirect
20. #41×C521C22semidirect
21. #41×C521C22semidirect
22. C2×Q8×C521C22semidirect
23. C2×D4×C521C22semidirect
24. C22×C4×C521C22semidirect
55. C521#585semidirect
63. C2×#41D521semidirect
70. #41C2×D521semidirect
71. #41C2×D521semidirect
74. C2×Q8C2×D521semidirect
78. C2×D4C2×D521semidirect
80. C22×C4C2×D521semidirect

Maximal subgroups

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

subgroupindex
#306597562
#306597552
#306597542
#306597532
C2×#225523642
#41×D5212
C2×#41×C5212
#585521