Finite Group Databasebeta

← #50306078

Subgroups — #50306078

Order 38336.

198 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 39 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#34062760C211yesmaximal, characteristic, complemented
2#34062685C212yesmaximal, complemented
3#34062683C211yesmaximal, characteristic, complemented
4#34062629C212yesmaximal, complemented
5#99×C599C211yesmaximal, characteristic, complemented
6C23×D599C2211yescharacteristic, complemented
7#23751078—21no—
8#23751077—22no—
9C2×D2396—22no—
10C2×C22⋊D599—21no—
11C2×C22⋊D599—21no—
12C2×C22⋊D599C2212yes—
13D4×D599—22no—
14C22⋊Dic599C2211yescharacteristic, complemented
15(C2×D599)⋊C4—22no—
16(C2×D599)⋊C4—21no—
17C2×D4×C599C2211yescharacteristic
18C22⋊C4×C599C2212yescomplemented
19C22×D599—21no—
20C22×D599—22no—
21C22×D599—21no—
22C22×D599—42no—
23C22×D599D412yescomplemented
24Dic1198—21no—
25D2396—21no—
26D2396—44no—
27C22⋊D599—22no—
28C22⋊D599—22no—
29C22⋊D599—22no—
30C22⋊D599—42no—
31C2×Dic599—21no—
32C2×Dic599—21no—
33C2×Dic599D412yescomplemented
34C4×D599—22no—
35C23×C599D411yescharacteristic, complemented
36C23×C599C2311yescharacteristic
37D4×C599—22no—
38C2×C4×C599—22no—
39C2×C4×C599D411yescharacteristic, complemented
40C22×C599—21no—
41C22×C599—41no—
42C22×C599—41no—
43C22×C599C2×D412yes—
44C22×C599C2×D411yescharacteristic
45C2×D599—22no—
46C2×D599—24no—
47C2×D599—22no—
48C2×D599—41no—
49C2×D599—42no—
50C2×D599—41no—
51C2×D599—42no—
52C2×D599—81no—
53C4×C599—21no—
54C4×C599—42no—
55Dic599—22no—
56Dic599—41no—
57C2×C599—21no—
58C2×C599—22no—
59C2×C599—41no—
60C2×C599#12011yescharacteristic
61D599—42no—
62D599—42no—
63C599B(4,𝔽2)11yescharacteristic, complemented, Sylow
64B(4,𝔽2)—5991nomaximal, Sylow
65H(5,𝔽2)—5991no—
66#120—5991no—
67#120—5992no—
68#99—5992no—
69#99D59911yescharacteristic, complemented
70C24—5991no—
71#41—11982no—
72#41—11981no—
73C2×D4—5992no—
74C2×D4—11982no—
75C2×D4—11982no—
76C2×D4—11981no—
77C2×D4—11981no—
78C2×D4C2×D59911yescharacteristic
79C22⋊C4—5991no—
80C22⋊C4—11982no—
81C22⋊C4—11981no—
82C22⋊C4C2×D59912yescomplemented
83C23—5992no—
84C23—23962no—
85C23—11981no—
86C23—11982no—
87C23—11981no—
88C23D239611yescharacteristic, complemented
89C23C22×D59911yescharacteristic
90Q8—11981no—
91D4—22no—
92D4—23964no—
93D4—23962no—
94D4—11981no—
95D4—11982no—
96D4—11982no—
97D4—11982no—
98C2×C4—22no—
99C2×C4—5992no—
100C2×C4—11982no—
101C2×C4—11981no—
102C2×C4—11981no—
103C2×C4D239611yescharacteristic, complemented
104C22—21no—
105C22—41no—
106C22—41no—
107C22—23962no—
108C22—23962no—
109C22—23961no—
110C22—23961no—
111C22—11984no—
112C22—11982no—
113C22—11982no—
114C22—47921no—
115C22D4×D59912yes—
116C22C2×D239611yescharacteristic
117C4—21no—
118C4—42no—
119C4—23961no—
120C4—11982no—
121C2—22no—
122C2—21no—
123C2—41no—
124C2—23962no—
125C2—23962no—
126C2#3406268511yescharacteristic
subgroupG/H
centerC2#34062685
commutator, cosocleC23×C599C23
FrattiniC23C22×D599
Fitting#99×C599C2
socleC2×C599#120
hypercenter#99D599
hypocenterC599B(4,𝔽2)
LCSG ▷ C23×C599 ▷ C2×C599 ▷ C599
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
1. #34062760C2semidirect
2. #34062685C2semidirect
3. #34062683C2semidirect
4. #34062629C2semidirect
5. #99×C599C2semidirect
6. C23×D599C22semidirect
14. C22⋊Dic599C22semidirect
18. C22⋊C4×C599C22semidirect
23. C22×D599D4semidirect
33. C2×Dic599D4semidirect
35. C23×C599D4semidirect
39. C2×C4×C599D4semidirect
63. C599B(4,𝔽2)semidirect
69. #99D599semidirect
82. C22⋊C4C2×D599semidirect
88. C23D2396semidirect
103. C2×C4D2396semidirect

Maximal subgroups

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

subgroupindex
#340627602
#340626852
#340626832
#340626292
#99×C5992
B(4,𝔽2)599