Finite Group Databasebeta

← #14558334

Subgroups — #14558334

Order 2368.

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#11924581C212yesmaximal, complemented
2#11924562C212yesmaximal, complemented
3#11924560C214yesmaximal, complemented
4#11924558C211yesmaximal, characteristic, complemented
5#11924555C212yesmaximal, complemented
6D8×D37C212yesmaximal, complemented
7#11924542C211yesmaximal, characteristic, complemented
8C2×D8×C37C211yesmaximal, characteristic, complemented
9C2×D4×C37C2212yescomplemented
10C2×C22⋊D37—24no—
11#10596964—22no—
12#10596964C2214yescomplemented
13D4×D37—22no—
14D4×D37C2214yescomplemented
15#10596962C2211yescharacteristic
16#10596962C2212yescomplemented
17D8×C37C2212yescomplemented
18D8×C37C2212yescomplemented
19C2×C8×C37C2211yescharacteristic, complemented
20#10596940C2214yescomplemented
21#10596939C2214yescomplemented
22#10596934C2211yescharacteristic, complemented
23Dic148C2211yescharacteristic, complemented
24D296C2211yescharacteristic, complemented
25#10596930C2212yescomplemented
26#10596929C2212yescomplemented
27C8×D37C2212yescomplemented
28C23×C37—22no—
29C22×D37—24no—
30D4×C37—22no—
31D4×C37C2314yes—
32C2×C4×C37C2311yescharacteristic
33C22⋊D37—22no—
34C22⋊D37—24no—
35C22⋊D37—24no—
36C22⋊D37D412yes—
37C2×Dic37—24no—
38D148D411yescharacteristic
39D148C2312yes—
40C4×D37—22no—
41C4×D37C2312yes—
42Dic74D411yescharacteristic
43Dic74C2312yes—
44C8×C37C2311yescharacteristic
45C8×C37C2311yescharacteristic
46#64436C2312yes—
47C22×C37—24no—
48C22×C37—82no—
49C22×C37C2×D411yescharacteristic
50C2×D37—22no—
51C2×D37—84no—
52C2×D37C2×D412yes—
53C4×C37C2×D411yescharacteristic
54C4×C37C2411yescharacteristic
55Dic37—22no—
56Dic37C2×D412yes—
57C2×C37—21no—
58C2×C37—44no—
59C2×C37C22×D411yescharacteristic
60D37—22no—
61D37—42no—
62#576—371nomaximal, Sylow
63C37#57611yescharacteristic, complemented, Sylow
64H(5,𝔽2)—372no—
65AGL(1,ℤ/8)—372no—
66AGL(1,ℤ/8)—374no—
67#135—372no—
68#135—371no—
69C2×D8—372no—
70C2×D8D3711yescharacteristic, complemented
71#131—371no—
72#41—371no—
73#41—374no—
74#41—372no—
75#41—742no—
76C2×D4—374no—
77C2×D4—742no—
78C2×D4—744no—
79C2×D4C2×D3712yescomplemented
80Q16—371no—
81SD16—374no—
82SD16—372no—
83D8—374no—
84D8—371no—
85D8C2×D3712yescomplemented
86D8C2×D3712yescomplemented
87M16—371no—
88M16—372no—
89C2×C8—372no—
90C2×C8C2×D3711yescharacteristic, complemented
91C23—22no—
92C23—744no—
93Q8—371no—
94Q8—372no—
95D4—22no—
96D4—372no—
97D4—371no—
98D4—372no—
99D4—744no—
100D4—744no—
101D4—742no—
102D4C22×D3714yes—
103C2×C4—372no—
104C2×C4—744no—
105C2×C4—742no—
106C2×C4C22×D3711yescharacteristic
107C8—372no—
108C8C22×D3711yescharacteristic
109C8C22×D3711yescharacteristic
110C22—24no—
111C22—82no—
112C22—372no—
113C22—2964no—
114C22—742no—
115C22D4×D3711yescharacteristic
116C4—372no—
117C4—742no—
118C4D4×D3711yescharacteristic
119C4C23×D3711yescharacteristic
120C2—21no—
121C2—44no—
122C2—742no—
123C2—1482no—
124C2C2×D4×D3711yescharacteristic
subgroupG/H
centerC2C2×D4×D37
commutator, cosocleC4×C37C24
FrattiniC4C23×D37
FittingC2×D8×C37C2
socleC2×C37C22×D4
hypercenterC2×D8D37
hypocenterC37#576
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #11924581C2semidirect
2. #11924562C2semidirect
3. #11924560C2semidirect
4. #11924558C2semidirect
5. #11924555C2semidirect
6. D8×D37C2semidirect
7. #11924542C2semidirect
8. C2×D8×C37C2semidirect
9. C2×D4×C37C22semidirect
12. #10596964C22semidirect
14. D4×D37C22semidirect
16. #10596962C22semidirect
17. D8×C37C22semidirect
18. D8×C37C22semidirect
19. C2×C8×C37C22semidirect
20. #10596940C22semidirect
21. #10596939C22semidirect
22. #10596934C22semidirect
23. Dic148C22semidirect
24. D296C22semidirect
25. #10596930C22semidirect
26. #10596929C22semidirect
27. C8×D37C22semidirect
63. C37#576semidirect
70. C2×D8D37semidirect
79. C2×D4C2×D37semidirect
85. D8C2×D37semidirect
86. D8C2×D37semidirect
90. C2×C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
#119245812
#119245622
#119245602
#119245582
#119245552
D8×D372
#119245422
C2×D8×C372
#57637