Finite Group Databasebeta

← #50306074

Subgroups — #50306074

Order 38336.

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

normal subgroups only

This group has 142 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#34062762C211yesmaximal, characteristic
2#34062748C211yesmaximal, characteristic, complemented
3#34062745C211yesmaximal, characteristic, complemented
4#34062715C211yesmaximal, characteristic, complemented
5#34062643C211yesmaximal, characteristic, complemented
6#34062633C211yesmaximal, characteristic, complemented
7#104×C599C211yesmaximal, characteristic, complemented
8#23751078—21no—
9#23751078C2211yescharacteristic
10#23751077—22no—
11#23751077—21no—
12C2×Dic1198—21no—
13C2×Dic1198C2211yescharacteristic
14C2×Dic1198C2211yescharacteristic
15Q8×D599—21no—
16Dic2396—21no—
17#23751068—21no—
18#23751067—21no—
19#23751066—21no—
20#23751062C2211yescharacteristic
21C4⋊Dic599—22no—
22#41×C599C2211yescharacteristic
23M16×C599C2211yescharacteristic
24C42×C599C2211yescharacteristic
25Dic1198—22no—
26Dic1198—21no—
27Dic1198—21no—
28Dic1198—21no—
29Dic1198—21no—
30Dic1198D411yescharacteristic
31D2396D411yescharacteristic
32C22⋊D599—22no—
33C22⋊D599—21no—
34C2×Dic599—22no—
35C2×Dic599—21no—
36C2×Dic599D412yes—
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—21no—
50C4×C599—22no—
51C4×C599—21no—
52C4×C599C2×D411yescharacteristic
53C4×C599C2×D411yescharacteristic
54Dic599—21no—
55Dic599—22no—
56Dic599—41no—
57C2×C599—21no—
58C2×C599—41no—
59C2×C599#12011yescharacteristic
60D599—41no—
61C599#45611yescharacteristic, complemented, Sylow
62#456—5991nomaximal, Sylow
632−1+4—5991no—
64#137—5991no—
65#137—5991no—
66C4⋊Q8—5991no—
67#104—5991no—
68#104D59911yescharacteristic, complemented
69#101—5991no—
70#41—5991no—
71#41—11981no—
72#41—11982no—
73#41—11981no—
74#41C2×D59911yescharacteristic
75C2×Q8—5991no—
76C2×Q8—5991no—
77C2×Q8—11981no—
78C2×Q8—11981no—
79Q16—11981no—
80Q16—11981no—
81SD16—11981no—
82SD16—11981no—
83M16—5991no—
84M16C2×D59911yescharacteristic
85C4⋊C4—11982no—
86C42C2×D59911yescharacteristic
87Q8—5991no—
88Q8—11982no—
89Q8—11981no—
90Q8—11981no—
91Q8—11981no—
92Q8—11981no—
93Q8D239611yescharacteristic
94D4—21no—
95D4—5991no—
96D4—11982no—
97D4—11981no—
98D4D239611yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—5992no—
102C2×C4—11982no—
103C2×C4—11981no—
104C2×C4—11982no—
105C2×C4—11981no—
106C2×C4C22×D59911yescharacteristic
107C8—21no—
108C8—11981no—
109C22—21no—
110C22—11981no—
111C22D4×D59911yescharacteristic
112C4—22no—
113C4—21no—
114C4—23961no—
115C4—11982no—
116C4—11981no—
117C4D4×D59911yescharacteristic
118C4C2×D239611yescharacteristic
119C2—21no—
120C2—41no—
121C2—23961no—
122C2#3406268511yescharacteristic
subgroupG/H
centerC2#34062685
commutator, cosocleC2×C4×C599C23
FrattiniC2×C4C22×D599
Fitting#104×C599C2
socleC2×C599#120
prime radical#34062762C2
hypercenter#104D599
hypocenterC599#456
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. #34062715C2semidirect
5. #34062643C2semidirect
6. #34062633C2semidirect
7. #104×C599C2semidirect
61. C599#456semidirect
68. #104D599semidirect

Maximal subgroups

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

subgroupindex
#340627622
#340627482
#340627452
#340627152
#340626432
#340626332
#104×C5992
#456599