Finite Group Databasebeta

← #50306069

Subgroups — #50306069

Order 38336.

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

normal subgroups only

This group has 152 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#34062761C211yesmaximal, characteristic
2#34062748C211yesmaximal, characteristic, complemented
3#34062745C211yesmaximal, characteristic, complemented
4#34062703C211yesmaximal, characteristic, complemented
5#34062643C211yesmaximal, characteristic, complemented
6#34062631C211yesmaximal, characteristic, complemented
7#104×C599C211yesmaximal, characteristic, complemented
8#23751079—21no—
9#23751078—21no—
10#23751078C2211yescharacteristic
11C2×Dic1198C2211yescharacteristic, complemented
12C2×D2396—21no—
13C2×D2396C2211yescharacteristic
14D4×D599—22no—
15D4×D599—21no—
16Dic2396—21no—
17#23751068—21no—
18#23751067—21no—
19#23751066—21no—
20#23751062C2211yescharacteristic, complemented
21(C2×D599)⋊C4—22no—
22#41×C599C2211yescharacteristic
23M16×C599C2211yescharacteristic, complemented
24C42×C599C2211yescharacteristic, complemented
25C22×D599—22no—
26C22×D599D412yes—
27Dic1198—21no—
28Dic1198—21no—
29Dic1198D411yescharacteristic
30D2396—22no—
31D2396—21no—
32D2396—21no—
33D2396D411yescharacteristic
34C22⋊D599—22no—
35C22⋊D599—21no—
36C2×Dic599—21no—
37C4×D599—22no—
38C4×D599—21no—
39C599⋊C8—21no—
40Q8×C599D411yescharacteristic
41D4×C599—21no—
42D4×C599D411yescharacteristic
43C2×C4×C599—21no—
44C2×C4×C599—21no—
45C2×C4×C599C2311yescharacteristic
46C8×C599—21no—
47C22×C599—21no—
48C22×C599C2×D411yescharacteristic
49C2×D599—22no—
50C2×D599—21no—
51C2×D599—42no—
52C2×D599—82no—
53C4×C599—21no—
54C4×C599—41no—
55C4×C599C2×D411yescharacteristic
56C4×C599C2×D411yescharacteristic
57Dic599—21no—
58Dic599—41no—
59C2×C599—21no—
60C2×C599—41no—
61C2×C599#12011yescharacteristic
62D599—42no—
63D599—41no—
64C599#45511yescharacteristic, complemented, Sylow
65#455—5991nomaximal, Sylow
66H(5,𝔽2)—5991no—
67#137—5991no—
68#137—5991no—
69#124—5991no—
70#104—5991no—
71#104D59911yescharacteristic, complemented
72#100—5991no—
73#41—5991no—
74#41—11981no—
75#41—11981no—
76#41C2×D59911yescharacteristic
77C2×Q8—5991no—
78C2×D4—5991no—
79C2×D4—11981no—
80C2×D4—11982no—
81C2×D4—11981no—
82Q16—11981no—
83Q16—11981no—
84SD16—11981no—
85SD16—11981no—
86M16—5991no—
87M16C2×D59911yescharacteristic, complemented
88C22⋊C4—11982no—
89C42C2×D59911yescharacteristic, complemented
90C23—5992no—
91C23—11982no—
92Q8—5991no—
93Q8—11981no—
94Q8—11981no—
95Q8D239611yescharacteristic
96D4—21no—
97D4—5991no—
98D4—11982no—
99D4—11982no—
100D4—11981no—
101D4—11981no—
102D4—11981no—
103D4D239611yescharacteristic
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—11982no—
107C2×C4—11981no—
108C2×C4—11981no—
109C2×C4C22×D59911yescharacteristic
110C8—21no—
111C8—11981no—
112C22—21no—
113C22—23962no—
114C22—11981no—
115C22—11982no—
116C22—47922no—
117C22D4×D59911yescharacteristic
118C4—21no—
119C4—41no—
120C4—23961no—
121C4—11981no—
122C4D4×D59911yescharacteristic
123C4C2×D239611yescharacteristic
124C2—21no—
125C2—41no—
126C2—23962no—
127C2—23961no—
128C2#3406268511yescharacteristic
subgroupG/H
centerC2#34062685
commutator, cosocleC2×C4×C599C23
FrattiniC2×C4C22×D599
Fitting#104×C599C2
socleC2×C599#120
prime radical#34062761C2
hypercenter#104D599
hypocenterC599#455
LCSG ▷ C2×C4×C599 ▷ C2×C599 ▷ C599
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #34062748C2semidirect
3. #34062745C2semidirect
4. #34062703C2semidirect
5. #34062643C2semidirect
6. #34062631C2semidirect
7. #104×C599C2semidirect
11. C2×Dic1198C22semidirect
20. #23751062C22semidirect
23. M16×C599C22semidirect
24. C42×C599C22semidirect
64. C599#455semidirect
71. #104D599semidirect
87. M16C2×D599semidirect
89. C42C2×D599semidirect

Maximal subgroups

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

subgroupindex
#340627612
#340627482
#340627452
#340627032
#340626432
#340626312
#104×C5992
#455599