Finite Group Databasebeta

← #34094988

Subgroups — #34094988

Order 20032.

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#23756545C212yesmaximal, complemented
2#23756544C214yesmaximal, complemented
3#23756543C214yesmaximal, complemented
4#23756542C216yesmaximal, complemented
5C2×#19097561C216yesmaximal, complemented
6#41×D313C218yesmaximal, complemented
7C2×#41×C313C211yesmaximal, characteristic, complemented
8#19097562C2218yescomplemented
9#19097561C22112yescomplemented
10#19097561C22112yescomplemented
11#19097561C22112yescomplemented
12#19097561C2214yescomplemented
13#19097560C22124yescomplemented
14C2×Dic626C2216yescomplemented
15Q8×D313C2218yescomplemented
16C2×D1252C2216yescomplemented
17C2×C22⋊D313C22112yescomplemented
18D4×D313C22124yescomplemented
19C2×C4×D313C22112yescomplemented
20#41×C313C2214yescomplemented
21#41×C313C2214yescomplemented
22C2×Q8×C313C2211yescharacteristic, complemented
23C2×D4×C313C2213yescomplemented
24C22×C4×C313C2213yescomplemented
25C22×D313C23112yes—
26Dic626C23112yes—
27Dic626C2314yes—
28D1252C23112yes—
29D1252C2314yes—
30C22⋊D313C23124yes—
31C22⋊D313C2318yes—
32C2×Dic313C23112yes—
33C4×D313C2318yes—
34C4×D313C23124yes—
35C23×C313C2313yes—
36Q8×C313C2314yes—
37D4×C313C23112yes—
38C2×C4×C313C2311yescharacteristic
39C2×C4×C313C2313yes—
40C2×C4×C313C2316yes—
41C2×C4×C313C2316yes—
42C22×C313—43no—
43C22×C313C2411yescharacteristic
44C22×C313C2416yes—
45C2×D313—412no—
46C2×D313C2418yes—
47C4×C313C2411yescharacteristic
48C4×C313C2416yes—
49C4×C313C2411yescharacteristic
50Dic313C2418yes—
51C2×C313—26no—
52C2×C313—21no—
53C2×C313C2511yescharacteristic
54D313—28no—
55C313#58511yescharacteristic, complemented, Sylow
56#585—3131nomaximal, Sylow
572−1+4—3134no—
582−1+4—3132no—
59H(5,𝔽2)—3134no—
60H(5,𝔽2)—3136no—
61C2×#41—3138no—
62C2×#41—3136no—
63C2×#41D31311yescharacteristic, complemented
64#41—3138no—
65#41—31324no—
66#41—31312no—
67#41—3134no—
68#41—31312no—
69#41—31312no—
70#41C2×D31314yescomplemented
71#41C2×D31314yescomplemented
72C2×Q8—3138no—
73C2×Q8—3136no—
74C2×Q8C2×D31311yescharacteristic, complemented
75C2×D4—31312no—
76C2×D4—31324no—
77C2×D4—3136no—
78C2×D4C2×D31313yescomplemented
79C22×C4—31312no—
80C22×C4C2×D31313yescomplemented
81C23—31312no—
82C23C22×D31313yes—
83Q8—31312no—
84Q8—3134no—
85Q8C22×D31314yes—
86D4—31324no—
87D4—3138no—
88D4—31312no—
89D4—3134no—
90D4C22×D313112yes—
91C2×C4—31312no—
92C2×C4—31324no—
93C2×C4—3138no—
94C2×C4C22×D31316yes—
95C2×C4C22×D31313yes—
96C2×C4C22×D31316yes—
97C2×C4C22×D31311yescharacteristic
98C22—43no—
99C22—3138no—
100C22—125212no—
101C22C23×D31316yes—
102C22C23×D31311yescharacteristic
103C4—3138no—
104C4C23×D31316yes—
105C4C23×D31311yescharacteristic
106C4C23×D31311yescharacteristic
107C2—21no—
108C2—26no—
109C2—6268no—
110C2C24×D31311yescharacteristic
subgroupG/H
centerC4C23×D313
commutator, socle, cosocleC2×C313C25
FrattiniC2C24×D313
FittingC2×#41×C313C2
hypercenterC2×#41D313
hypocenterC313#585
LCSG ▷ C2×C313 ▷ C313
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #23756545C2semidirect
2. #23756544C2semidirect
3. #23756543C2semidirect
4. #23756542C2semidirect
5. C2×#19097561C2semidirect
6. #41×D313C2semidirect
7. C2×#41×C313C2semidirect
8. #19097562C22semidirect
9. #19097561C22semidirect
10. #19097561C22semidirect
11. #19097561C22semidirect
12. #19097561C22semidirect
13. #19097560C22semidirect
14. C2×Dic626C22semidirect
15. Q8×D313C22semidirect
16. C2×D1252C22semidirect
17. C2×C22⋊D313C22semidirect
18. D4×D313C22semidirect
19. C2×C4×D313C22semidirect
20. #41×C313C22semidirect
21. #41×C313C22semidirect
22. C2×Q8×C313C22semidirect
23. C2×D4×C313C22semidirect
24. C22×C4×C313C22semidirect
55. C313#585semidirect
63. C2×#41D313semidirect
70. #41C2×D313semidirect
71. #41C2×D313semidirect
74. C2×Q8C2×D313semidirect
78. C2×D4C2×D313semidirect
80. C22×C4C2×D313semidirect

Maximal subgroups

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

subgroupindex
#237565452
#237565442
#237565432
#237565422
C2×#190975612
#41×D3132
C2×#41×C3132
#585313