Finite Group Databasebeta

← #14558335

Subgroups — #14558335

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#11924582C212yesmaximal, complemented
2#11924563C214yesmaximal, complemented
3#11924561C212yesmaximal, complemented
4#11924559C212yesmaximal, complemented
5C2×D296C211yesmaximal, characteristic, complemented
6D8×D37C212yesmaximal, complemented
7#11924542C211yesmaximal, characteristic, complemented
8#135×C37C211yesmaximal, characteristic, complemented
9#41×C37C2212yescomplemented
10#10596966C2214yescomplemented
11D4×D37—24no—
12D4×D37C2214yescomplemented
13#10596962—22no—
14#10596962C2211yescharacteristic
15C2×D148—22no—
16C2×D148C2212yescomplemented
17Q16×C37C2211yescharacteristic, complemented
18SD16×C37C2212yescomplemented
19D8×C37C2211yescharacteristic, complemented
20C2×C8×C37C2211yescharacteristic, complemented
21#10596941C2214yescomplemented
22#10596939C2214yescomplemented
23#10596934C2211yescharacteristic, complemented
24D296C2212yescomplemented
25D296C2212yescomplemented
26#10596929C2212yescomplemented
27C8×D37C2212yescomplemented
28C22×D37—22no—
29C22×D37—24no—
30Q8×C37C2312yes—
31D4×C37—22no—
32D4×C37C2312yes—
33C2×C4×C37—22no—
34C2×C4×C37C2311yescharacteristic
35C22⋊D37—24no—
36C22⋊D37D412yes—
37D148—24no—
38D148—22no—
39D148D411yescharacteristic
40D148C2314yes—
41C4×D37—24no—
42C4×D37C2312yes—
43Dic74D411yescharacteristic
44C8×C37C2311yescharacteristic
45C8×C37C2311yescharacteristic
46#64436C2312yes—
47C22×C37—22no—
48C22×C37C2×D411yescharacteristic
49C2×D37—24no—
50C2×D37—84no—
51C2×D37—82no—
52C2×D37C2×D412yes—
53C4×C37—22no—
54C4×C37C2×D411yescharacteristic
55C4×C37C2411yescharacteristic
56Dic37C2×D412yes—
57C2×C37—21no—
58C2×C37—42no—
59C2×C37C22×D411yescharacteristic
60D37—22no—
61D37—44no—
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#135D3711yescharacteristic, complemented
69C2×D8—372no—
70C2×D8—371no—
71#131—371no—
72#41—371no—
73#41—374no—
74#41—742no—
75#41C2×D3712yescomplemented
76C2×D4—374no—
77C2×D4—372no—
78C2×D4—742no—
79C2×D4—744no—
80Q16C2×D3711yescharacteristic, complemented
81SD16—374no—
82SD16C2×D3712yescomplemented
83D8—374no—
84D8—372no—
85D8—372no—
86D8C2×D3711yescharacteristic, complemented
87M16—371no—
88M16—372no—
89C2×C8—372no—
90C2×C8C2×D3711yescharacteristic, complemented
91C23—744no—
92C23—742no—
93Q8—371no—
94Q8C22×D3712yes—
95D4—22no—
96D4—372no—
97D4—371no—
98D4—374no—
99D4—744no—
100D4—744no—
101D4—742no—
102D4C22×D3712yes—
103C2×C4—22no—
104C2×C4—372no—
105C2×C4—744no—
106C2×C4C22×D3711yescharacteristic
107C8—372no—
108C8C22×D3711yescharacteristic
109C8C22×D3711yescharacteristic
110C22—22no—
111C22—372no—
112C22—2962no—
113C22—2964no—
114C22—744no—
115C22D4×D3711yescharacteristic
116C4—22no—
117C4—372no—
118C4D4×D3711yescharacteristic
119C4C23×D3711yescharacteristic
120C2—21no—
121C2—42no—
122C2—742no—
123C2—1484no—
124C2C2×D4×D3711yescharacteristic
subgroupG/H
centerC2C2×D4×D37
commutator, cosocleC4×C37C24
FrattiniC4C23×D37
Fitting#135×C37C2
socleC2×C37C22×D4
hypercenter#135D37
hypocenterC37#576
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #11924582C2semidirect
2. #11924563C2semidirect
3. #11924561C2semidirect
4. #11924559C2semidirect
5. C2×D296C2semidirect
6. D8×D37C2semidirect
7. #11924542C2semidirect
8. #135×C37C2semidirect
9. #41×C37C22semidirect
10. #10596966C22semidirect
12. D4×D37C22semidirect
16. C2×D148C22semidirect
17. Q16×C37C22semidirect
18. SD16×C37C22semidirect
19. D8×C37C22semidirect
20. C2×C8×C37C22semidirect
21. #10596941C22semidirect
22. #10596939C22semidirect
23. #10596934C22semidirect
24. D296C22semidirect
25. D296C22semidirect
26. #10596929C22semidirect
27. C8×D37C22semidirect
63. C37#576semidirect
68. #135D37semidirect
75. #41C2×D37semidirect
80. Q16C2×D37semidirect
82. SD16C2×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
#119245822
#119245632
#119245612
#119245592
C2×D2962
D8×D372
#119245422
#135×C372
#57637