Finite Group Databasebeta

← #50306081

Subgroups — #50306081

Order 38336.

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

normal subgroups only

This group has 160 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
2#34062699C212yesmaximal, complemented
3#34062696C211yesmaximal, characteristic, complemented
4#34062629C212yesmaximal, complemented
5#99×C599C211yesmaximal, characteristic, complemented
6#23751078—21no—
7#23751077—22no—
8C2×C22⋊D599—21no—
9C2×C22⋊D599C2212yes—
10D4×D599—22no—
11C22×Dic599C2211yescharacteristic, complemented
12C4⋊Dic599—22no—
13Dic599⋊C4—21no—
14C22⋊Dic599—21no—
15C22⋊Dic599C2211yescharacteristic, complemented
16(C2×D599)⋊C4—22no—
17C2×D4×C599C2211yescharacteristic
18C22⋊C4×C599C2212yescomplemented
19C22×D599—21no—
20C22×D599D412yes—
21Dic1198—21no—
22D2396—21no—
23C22⋊D599—22no—
24C22⋊D599—22no—
25C22⋊D599—22no—
26C2×Dic599—21no—
27C2×Dic599—22no—
28C2×Dic599—21no—
29C2×Dic599—21no—
30C2×Dic599D412yes—
31C4×D599—22no—
32C23×C599D411yescharacteristic
33C23×C599C2311yescharacteristic
34D4×C599—22no—
35C2×C4×C599—22no—
36C2×C4×C599D411yescharacteristic
37C22×C599—21no—
38C22×C599—41no—
39C22×C599—41no—
40C22×C599C2×D412yes—
41C22×C599C2×D411yescharacteristic
42C2×D599—22no—
43C2×D599—42no—
44C2×D599—81no—
45C4×C599—21no—
46C4×C599—42no—
47Dic599—22no—
48Dic599—41no—
49Dic599—41no—
50C2×C599—21no—
51C2×C599—22no—
52C2×C599—41no—
53C2×C599#12011yescharacteristic
54D599—42no—
55C599#45811yescharacteristic, complemented, Sylow
56#458—5991nomaximal, Sylow
57H(5,𝔽2)—5991no—
58#123—5991no—
59#123—5992no—
60#99—5992no—
61#99D59911yescharacteristic, complemented
62#41—11982no—
63#41—11981no—
64C2×D4—5992no—
65C2×D4—11982no—
66C2×D4—11981no—
67C2×D4C2×D59911yescharacteristic
68C22×C4—5991no—
69C4⋊C4—11982no—
70C4⋊C4—11981no—
71C22⋊C4—5991no—
72C22⋊C4—11982no—
73C22⋊C4—11981no—
74C22⋊C4C2×D59912yescomplemented
75C23—5992no—
76C23—11981no—
77C23D239611yescharacteristic
78C23C22×D59911yescharacteristic
79Q8—11981no—
80D4—22no—
81D4—11981no—
82D4—11982no—
83D4—11982no—
84D4—11982no—
85C2×C4—22no—
86C2×C4—5992no—
87C2×C4—11982no—
88C2×C4—11982no—
89C2×C4—11981no—
90C2×C4—11981no—
91C2×C4—11981no—
92C2×C4D239611yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—23962no—
97C22—11982no—
98C22—47921no—
99C22D4×D59912yes—
100C22C2×D239611yescharacteristic
101C4—21no—
102C4—42no—
103C4—23961no—
104C4—23961no—
105C4—11982no—
106C2—22no—
107C2—21no—
108C2—41no—
109C2—23962no—
110C2#3406268511yescharacteristic
subgroupG/H
centerC2#34062685
commutator, cosocleC23×C599C23
FrattiniC23C22×D599
Fitting#99×C599C2
socleC2×C599#120
prime radical#34062760C2
hypercenter#99D599
hypocenterC599#458
LCSG ▷ C23×C599 ▷ C2×C599 ▷ C599
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
2. #34062699C2semidirect
3. #34062696C2semidirect
4. #34062629C2semidirect
5. #99×C599C2semidirect
11. C22×Dic599C22semidirect
15. C22⋊Dic599C22semidirect
18. C22⋊C4×C599C22semidirect
55. C599#458semidirect
61. #99D599semidirect
74. C22⋊C4C2×D599semidirect

Maximal subgroups

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

subgroupindex
#340627602
#340626992
#340626962
#340626292
#99×C5992
#458599