Finite Group Databasebeta

← #13093219

Subgroups — #13093219

Order 1472.

268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 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#10625160C212yesmaximal, complemented
2C23×#135C211yesmaximal, characteristic, complemented
3#10625120C212yesmaximal, complemented
4#10625090C212yesmaximal, complemented
5#10625085C214yesmaximal, complemented
6D8×D23C212yesmaximal, complemented
7C2×D184C211yesmaximal, characteristic, complemented
8#10625072C211yesmaximal, characteristic, complemented
9#41×C23C2212yescomplemented
10#67292C2214yescomplemented
11D4×D23—24no—
12D4×D23C2214yescomplemented
13#67288—22no—
14#67288C2211yescharacteristic
15C2×D92—22no—
16C2×D92C2212yescomplemented
17Q16×C23C2211yescharacteristic, complemented
18SD16×C23C2212yescomplemented
19D8×C23C2211yescharacteristic, complemented
20C2×C8×C23C2211yescharacteristic, complemented
21#67274C2214yescomplemented
22#67272C2214yescomplemented
23#67267C2211yescharacteristic, complemented
24D184C2212yescomplemented
25D184C2212yescomplemented
26#67262C2212yescomplemented
27C8×D23C2212yescomplemented
28C22×D23—22no—
29C22×D23—24no—
30Q8×C23C2312yes—
31D4×C23—22no—
32D4×C23C2312yes—
33C2×C4×C23—22no—
34C2×C4×C23C2311yescharacteristic
35C22⋊D23—24no—
36C22⋊D23D412yes—
37D92—24no—
38D92—22no—
39D92D411yescharacteristic
40D92C2314yes—
41C4×D23—24no—
42C4×D23C2312yes—
43Dic46D411yescharacteristic
44C8×C23C2311yescharacteristic
45C8×C23C2311yescharacteristic
46C23⋊C8C2312yes—
47C22×C23—22no—
48C22×C23C2×D411yescharacteristic
49C2×D23—24no—
50C2×D23—84no—
51C2×D23—82no—
52C2×D23C2×D412yes—
53C4×C23—22no—
54C4×C23C2×D411yescharacteristic
55C4×C23C2411yescharacteristic
56Dic23C2×D412yes—
57#576—231nomaximal, Sylow
58C2×C23—21no—
59C2×C23—42no—
60C2×C23C22×D411yescharacteristic
61D23—22no—
62D23—44no—
63H(5,𝔽2)—232no—
64AGL(1,ℤ/8)—232no—
65AGL(1,ℤ/8)—234no—
66#135—232no—
67#135D2311yescharacteristic, complemented
68C2×D8—232no—
69C2×D8—231no—
70#131—231no—
71C23#57611yescharacteristic, complemented, Sylow
72#41—231no—
73#41—234no—
74#41—462no—
75#41C2×D2312yescomplemented
76C2×D4—234no—
77C2×D4—232no—
78C2×D4—462no—
79C2×D4—464no—
80Q16C2×D2311yescharacteristic, complemented
81SD16—234no—
82SD16C2×D2312yescomplemented
83D8—234no—
84D8—232no—
85D8—232no—
86D8C2×D2311yescharacteristic, complemented
87M16—231no—
88M16—232no—
89C2×C8—232no—
90C2×C8C2×D2311yescharacteristic, complemented
91C23—464no—
92C23—462no—
93Q8—231no—
94Q8C22×D2312yes—
95D4—22no—
96D4—232no—
97D4—231no—
98D4—234no—
99D4—464no—
100D4—464no—
101D4—462no—
102D4C22×D2312yes—
103C2×C4—22no—
104C2×C4—232no—
105C2×C4—464no—
106C2×C4C22×D2311yescharacteristic
107C8—232no—
108C8C22×D2311yescharacteristic
109C8C22×D2311yescharacteristic
110C22—22no—
111C22—232no—
112C22—464no—
113C22—1842no—
114C22—1844no—
115C22D4×D2311yescharacteristic
116C4—22no—
117C4—232no—
118C4D4×D2311yescharacteristic
119C4C23×D2311yescharacteristic
120C2—21no—
121C2—42no—
122C2—462no—
123C2—924no—
124C2C2×D4×D2311yescharacteristic
subgroupG/H
centerC2C2×D4×D23
commutator, cosocleC4×C23C24
FrattiniC4C23×D23
FittingC23×#135C2
socleC2×C23C22×D4
hypercenter#135D23
hypocenterC23#576
LCSG ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #10625160C2semidirect
2. C23×#135C2semidirect
3. #10625120C2semidirect
4. #10625090C2semidirect
5. #10625085C2semidirect
6. D8×D23C2semidirect
7. C2×D184C2semidirect
8. #10625072C2semidirect
9. #41×C23C22semidirect
10. #67292C22semidirect
12. D4×D23C22semidirect
16. C2×D92C22semidirect
17. Q16×C23C22semidirect
18. SD16×C23C22semidirect
19. D8×C23C22semidirect
20. C2×C8×C23C22semidirect
21. #67274C22semidirect
22. #67272C22semidirect
23. #67267C22semidirect
24. D184C22semidirect
25. D184C22semidirect
26. #67262C22semidirect
27. C8×D23C22semidirect
67. #135D23semidirect
71. C23#576semidirect
75. #41C2×D23semidirect
80. Q16C2×D23semidirect
82. SD16C2×D23semidirect
86. D8C2×D23semidirect
90. C2×C8C2×D23semidirect

Maximal subgroups

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

subgroupindex
#106251602
C23×#1352
#106251202
#106250902
#106250852
D8×D232
C2×D1842
#106250722
#57623