Finite Group Databasebeta

← #13093253

Subgroups — #13093253

Order 1472.

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
1C2×#41×C23C211yesmaximal, characteristic, complemented
2#10625161C214yesmaximal, complemented
3#10625160C214yesmaximal, complemented
4#41×D23C218yesmaximal, complemented
5#10625158C212yesmaximal, complemented
6#10625155C216yesmaximal, complemented
7C2×#67288C216yesmaximal, complemented
8#41×C23C2214yescomplemented
9#41×C23C2214yescomplemented
10C2×Q8×C23C2211yescharacteristic, complemented
11C2×D4×C23C2213yescomplemented
12C22×C4×C23C2213yescomplemented
13C2×C22⋊D23C22112yescomplemented
14#67292C2218yescomplemented
15Q8×D23C2218yescomplemented
16#67290C22124yescomplemented
17D4×D23C22124yescomplemented
18#67288C2214yescomplemented
19#67288C22112yescomplemented
20#67288C22112yescomplemented
21#67288C22112yescomplemented
22C2×D92C2216yescomplemented
23C2×C4×D23C22112yescomplemented
24C2×Dic46C2216yescomplemented
25C23×C23C2313yes—
26C22×D23C23112yes—
27Q8×C23C2314yes—
28D4×C23C23112yes—
29C2×C4×C23C2316yes—
30C2×C4×C23C2316yes—
31C2×C4×C23C2311yescharacteristic
32C2×C4×C23C2313yes—
33C22⋊D23C2318yes—
34C22⋊D23C23124yes—
35C2×Dic23C23112yes—
36D92C2314yes—
37D92C23112yes—
38C4×D23C2318yes—
39C4×D23C23124yes—
40Dic46C2314yes—
41Dic46C23112yes—
42C22×C23—43no—
43C22×C23C2416yes—
44C22×C23C2411yescharacteristic
45C2×D23—412no—
46C2×D23C2418yes—
47C4×C23C2411yescharacteristic
48C4×C23C2416yes—
49C4×C23C2411yescharacteristic
50Dic23C2418yes—
51#585—231nomaximal, Sylow
52C2×C23—26no—
53C2×C23—21no—
54C2×C23C2511yescharacteristic
55D23—28no—
562−1+4—234no—
572−1+4—232no—
58H(5,𝔽2)—234no—
59H(5,𝔽2)—236no—
60C2×#41—238no—
61C2×#41—236no—
62C2×#41D2311yescharacteristic, complemented
63C23#58511yescharacteristic, complemented, Sylow
64#41—238no—
65#41—2324no—
66#41—2312no—
67#41—234no—
68#41—2312no—
69#41—2312no—
70#41C2×D2314yescomplemented
71#41C2×D2314yescomplemented
72C2×Q8—238no—
73C2×Q8—236no—
74C2×Q8C2×D2311yescharacteristic, complemented
75C2×D4—2312no—
76C2×D4—2324no—
77C2×D4—236no—
78C2×D4C2×D2313yescomplemented
79C22×C4—2312no—
80C22×C4C2×D2313yescomplemented
81C23—2312no—
82C23C22×D2313yes—
83Q8—2312no—
84Q8—234no—
85Q8C22×D2314yes—
86D4—2324no—
87D4—238no—
88D4—2312no—
89D4—234no—
90D4C22×D23112yes—
91C2×C4—2312no—
92C2×C4—2324no—
93C2×C4—238no—
94C2×C4C22×D2316yes—
95C2×C4C22×D2313yes—
96C2×C4C22×D2316yes—
97C2×C4C22×D2311yescharacteristic
98C22—43no—
99C22—238no—
100C22—9212no—
101C22C23×D2316yes—
102C22C23×D2311yescharacteristic
103C4—238no—
104C4C23×D2316yes—
105C4C23×D2311yescharacteristic
106C4C23×D2311yescharacteristic
107C2—21no—
108C2—26no—
109C2—468no—
110C2C24×D2311yescharacteristic
subgroupG/H
centerC4C23×D23
commutator, socle, cosocleC2×C23C25
FrattiniC2C24×D23
FittingC2×#41×C23C2
hypercenterC2×#41D23
hypocenterC23#585
LCSG ▷ C2×C23 ▷ C23
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#41×C23C2semidirect
2. #10625161C2semidirect
3. #10625160C2semidirect
4. #41×D23C2semidirect
5. #10625158C2semidirect
6. #10625155C2semidirect
7. C2×#67288C2semidirect
8. #41×C23C22semidirect
9. #41×C23C22semidirect
10. C2×Q8×C23C22semidirect
11. C2×D4×C23C22semidirect
12. C22×C4×C23C22semidirect
13. C2×C22⋊D23C22semidirect
14. #67292C22semidirect
15. Q8×D23C22semidirect
16. #67290C22semidirect
17. D4×D23C22semidirect
18. #67288C22semidirect
19. #67288C22semidirect
20. #67288C22semidirect
21. #67288C22semidirect
22. C2×D92C22semidirect
23. C2×C4×D23C22semidirect
24. C2×Dic46C22semidirect
62. C2×#41D23semidirect
63. C23#585semidirect
70. #41C2×D23semidirect
71. #41C2×D23semidirect
74. C2×Q8C2×D23semidirect
78. C2×D4C2×D23semidirect
80. C22×C4C2×D23semidirect

Maximal subgroups

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

subgroupindex
C2×#41×C232
#106251612
#106251602
#41×D232
#106251582
#106251552
C2×#672882
#58523