Finite Group Databasebeta

← #50306632

Subgroups — #50306632

Order 38336.

260 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 91 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#34062704C212yesmaximal, complemented
2#34062703C212yesmaximal, complemented
3#34062701C214yesmaximal, complemented
4#34062685C214yesmaximal, complemented
5#34062683C212yesmaximal, complemented
6#124×C599C211yesmaximal, characteristic, complemented
7C23×D599C2212yescomplemented
8C2×Dic1198C2212yescomplemented
9C2×D2396C2212yes—
10C2×D2396C2212yes—
11C2×C22⋊D599C2214yes—
12C22⋊Dic599C2212yescomplemented
13(C2×D599)⋊C4C2214yescomplemented
14(C2×D599)⋊C4C2214yescomplemented
15(C2×D599)⋊C4C2214yescomplemented
16C4×Dic599C2212yescomplemented
17C2×Q8×C599C2211yescharacteristic, complemented
18C2×D4×C599C2211yescharacteristic
19C22⋊C4×C599C2214yescomplemented
20C42×C599C2211yescharacteristic, complemented
21C22×D599—44no—
22C22×D599—42no—
23C22×D599C2314yes—
24Dic1198—42no—
25D2396—42no—
26D2396—42no—
27C22⋊D599—44no—
28C2×Dic599C2314yes—
29C23×C599C2312yes—
30Q8×C599—41no—
31D4×C599—41no—
32C2×C4×C599C2312yes—
33C2×C4×C599C2311yescharacteristic
34C2×C4×C599C2312yes—
35C22×C599—22no—
36C22×C599—24no—
37C22×C599C2411yescharacteristic
38C2×D599—24no—
39C2×D599—24no—
40C2×D599—24no—
41C2×D599—48no—
42C4×C599—21no—
43C4×C599—22no—
44C4×C599—22no—
45Dic599—24no—
46C2×C599—42no—
47C2×C599H(5,𝔽2)11yescharacteristic
48C2×C599H(5,𝔽2)12yes—
49D599—44no—
50C599H(3,𝔽4)11yescharacteristic, complemented, Sylow
51H(3,𝔽4)—5991nomaximal, Sylow
52#124—5992no—
53#124—5994no—
54#124—5992no—
55#124D59911yescharacteristic, complemented
56#120—5992no—
57#120—5994no—
58C24—5992no—
59C2×Q8—5992no—
60C2×Q8C2×D59911yescharacteristic, complemented
61C2×D4—5994no—
62C2×D4—5992no—
63C2×D4—5992no—
64C2×D4C2×D59911yescharacteristic
65C22⋊C4—5992no—
66C22⋊C4—5994no—
67C22⋊C4—5994no—
68C22⋊C4—5994no—
69C22⋊C4C2×D59914yescomplemented
70C42—5992no—
71C42C2×D59911yescharacteristic, complemented
72C23—5994no—
73C23—23962no—
74C23—23964no—
75C23C22×D59912yes—
76Q8—41no—
77Q8—23962no—
78D4—41no—
79D4—23962no—
80D4—23962no—
81D4—23964no—
82C2×C4—5994no—
83C2×C4C22×D59912yes—
84C2×C4C22×D59911yescharacteristic
85C2×C4C22×D59912yes—
86C22—22no—
87C22—24no—
88C22—23968no—
89C22—11984no—
90C22—11984no—
91C22—11984no—
92C22C23×D59911yescharacteristic
93C4—21no—
94C4—22no—
95C4—22no—
96C4—11984no—
97C2—42no—
98C2—23964no—
99C2#3406276011yescharacteristic
100C2#3406276112yes—
subgroupG/H
center, FrattiniC22C23×D599
commutator, socle, cosocleC22×C599C24
Fitting#124×C599C2
hypercenter#124D599
hypocenterC599H(3,𝔽4)
LCSG ▷ C22×C599 ▷ C599
UCSC1 ◁ C22 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #34062704C2semidirect
2. #34062703C2semidirect
3. #34062701C2semidirect
4. #34062685C2semidirect
5. #34062683C2semidirect
6. #124×C599C2semidirect
7. C23×D599C22semidirect
8. C2×Dic1198C22semidirect
12. C22⋊Dic599C22semidirect
13. (C2×D599)⋊C4C22semidirect
14. (C2×D599)⋊C4C22semidirect
15. (C2×D599)⋊C4C22semidirect
16. C4×Dic599C22semidirect
17. C2×Q8×C599C22semidirect
19. C22⋊C4×C599C22semidirect
20. C42×C599C22semidirect
50. C599H(3,𝔽4)semidirect
55. #124D599semidirect
60. C2×Q8C2×D599semidirect
69. C22⋊C4C2×D599semidirect
71. C42C2×D599semidirect

Maximal subgroups

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

subgroupindex
#340627042
#340627032
#340627012
#340626852
#340626832
#124×C5992
H(3,𝔽4)599