Finite Group Databasebeta

← #20242700

Subgroups — #20242700

Order 6016.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#15689873C211yesmaximal, characteristic
2#15689532C212yesmaximal, complemented
3#15689518C211yesmaximal, characteristic
4#15688864C212yesmaximal, complemented
5C47×#329C211yesmaximal, characteristic
6C2×#10625337—21no—
7C2×#10625335—21no—
8#13094024C2211yescharacteristic
9#13094022—21no—
10#13094017—22no—
11#13094016C2212yes—
12#13094005—21no—
13#13094001—22no—
14#13093958—22no—
15#13093956—22no—
16#13093935C2211yescharacteristic
17#124×C47C2211yescharacteristic
18#97×C47C2212yes—
19C2×Q8×C47D411yescharacteristic
20C2×D4×C47D411yescharacteristic
21C22×Dic47—21no—
22C2×Dic94—21no—
23C2×Dic94—21no—
24C2×C8×C47—22no—
25C22⋊C4×C47—22no—
26C42×C47C2311yescharacteristic
27C22⋊Dic47—22no—
28C22⋊Dic47—21no—
29#10625337—42no—
30#10625335—42no—
31C4⋊Dic47—22no—
32C4⋊Dic47D412yes—
33C4⋊Dic47D412yes—
34Dic47⋊C4—22no—
35Dic47⋊C4—22no—
36Dic47⋊C4—22no—
37C4×Dic47—21no—
38C2×C47⋊C8—21no—
39C23×C47—21no—
40Q8×C47—41no—
41D4×C47—41no—
42C2×C4×C47—21no—
43C2×C4×C47C2×D411yescharacteristic
44C2×C4×C47C2×D412yes—
45C2×Dic47—22no—
46C2×Dic47—22no—
47C2×Dic47—41no—
48C2×Dic47—81no—
49Dic94—41no—
50Dic94—41no—
51Dic94—81no—
52C8×C47—24no—
53C47⋊C8—22no—
54C22×C47—41no—
55C22×C47—42no—
56C22×C47#12011yescharacteristic
57C4×C47—21no—
58C4×C47—22no—
59C4×C47—41no—
60Dic47—42no—
61Dic47—42no—
62Dic47—81no—
63#1660—471nomaximal, Sylow
64C2×C47—81no—
65C2×C47#45311yescharacteristic
66C2×C47#45612yes—
67#563—471no—
68#501—472no—
69#497—471no—
70#330—472no—
71#329D4711yescharacteristic
72C47#166011yescharacteristic, complemented, Sylow
73C2×Q16—941no—
74C2×SD16—941no—
75C4⋊Q8—471no—
76C4⋊Q8—941no—
77#126—942no—
78#125—472no—
79#124C2×D4711yescharacteristic
80#123—941no—
81C22⋊Q8—942no—
82#107—942no—
83#106—942no—
84#97—471no—
85#97C2×D4712yes—
86C2×Q8—941no—
87C2×Q8—941no—
88C2×Q8D18811yescharacteristic
89C2×D4D18811yescharacteristic
90C22×C4—941no—
91Q16—1882no—
92SD16—1882no—
93C2×C8—22no—
94C2×C8—941no—
95C4⋊C4—472no—
96C4⋊C4—472no—
97C4⋊C4—942no—
98C4⋊C4—942no—
99C4⋊C4—942no—
100C4⋊C4—942no—
101C22⋊C4—22no—
102C22⋊C4—942no—
103C22⋊C4—941no—
104C42—941no—
105C42C22×D4711yescharacteristic
106C23—21no—
107Q8—41no—
108Q8—3761no—
109Q8—1881no—
110Q8—1881no—
111D4—41no—
112C2×C4—21no—
113C2×C4—942no—
114C2×C4—942no—
115C2×C4—3761no—
116C2×C4—1881no—
117C2×C4C2×D18811yescharacteristic
118C2×C4D4×D4712yes—
119C8—24no—
120C8—942no—
121C22—41no—
122C22—42no—
123C22#1309399411yescharacteristic
124C4—21no—
125C4—22no—
126C4—41no—
127C4—3761no—
128C4—1882no—
129C4—1882no—
130C2—81no—
131C2#1568929311yescharacteristic
132C2#1568930712yes—
subgroupG/H
centerC22#13093994
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#329C2
socleC22×C47#120
hypercenter#329D47
hypocenterC47#1660
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #15689532C2semidirect
4. #15688864C2semidirect
72. C47#1660semidirect