Finite Group Databasebeta

← #20242687

Subgroups — #20242687

Order 6016.

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

normal subgroups only

This group has 206 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, complemented
2#15689513C211yesmaximal, characteristic
3#15689488C212yesmaximal, complemented
4#15688864C212yesmaximal, complemented
5C47×#329C211yesmaximal, characteristic, complemented
6C2×#10625336—21no—
7C2×#10625334—21no—
8#13094022—21no—
9#13094021C2211yescharacteristic
10#13094017—22no—
11#13094016C2212yes—
12#13094005—21no—
13#13094001—22no—
14#13093946—22no—
15#13093946—22no—
16#13093935C2211yescharacteristic
17#124×C47C2211yescharacteristic
18#97×C47C2212yes—
19C2×Q8×C47D411yescharacteristic
20C2×D4×C47D411yescharacteristic
21C22×Dic47—21no—
22C2×D188—22no—
23C2×D188—21no—
24C2×Dic94—21no—
25C2×C8×C47—22no—
26C22⋊C4×C47—22no—
27C42×C47C2311yescharacteristic
28C22⋊Dic47—22no—
29C22⋊Dic47—21no—
30#10625336—42no—
31#10625334—42no—
32C4⋊Dic47D412yes—
33C4⋊Dic47D412yes—
34Dic47⋊C4—22no—
35Dic47⋊C4—22no—
36Dic47⋊C4—22no—
37C4×Dic47—21no—
38C2×C47⋊C8—21no—
39C23×C47—21no—
40C22×D47—41no—
41Q8×C47—41no—
42D4×C47—41no—
43C2×C4×C47—21no—
44C2×C4×C47C2×D411yescharacteristic
45C2×C4×C47C2×D412yes—
46C2×Dic47—22no—
47C2×Dic47—22no—
48C2×Dic47—81no—
49D188—41no—
50D188—41no—
51D188—44no—
52Dic94—81no—
53C8×C47—42no—
54C47⋊C8—22no—
55C22×C47—41no—
56C22×C47—42no—
57C22×C47#12011yescharacteristic
58C2×D47—81no—
59C2×D47—82no—
60C4×C47—21no—
61C4×C47—22no—
62C4×C47—41no—
63Dic47—42no—
64Dic47—42no—
65#1657—471nomaximal, Sylow
66C2×C47—81no—
67C2×C47#45311yescharacteristic
68C2×C47#45412yes—
69D47—161no—
70#563—471no—
71#496—471no—
72#490—472no—
73#330—472no—
74#329D4711yescharacteristic, complemented
75C47#165711yescharacteristic, complemented, Sylow
76C2×SD16—941no—
77C2×D8—941no—
78C4⋊Q8—941no—
79#127—471no—
80#126—942no—
81#125—472no—
82#124C2×D4711yescharacteristic
83#123—941no—
84C22⋊Q8—942no—
85#102—942no—
86#102—942no—
87#97—471no—
88#97C2×D4712yes—
89C2×Q8—941no—
90C2×Q8D18811yescharacteristic
91C2×D4—941no—
92C2×D4—942no—
93C2×D4D18811yescharacteristic
94C22×C4—941no—
95SD16—1882no—
96D8—1882no—
97C2×C8—22no—
98C2×C8—941no—
99C4⋊C4—472no—
100C4⋊C4—472no—
101C4⋊C4—942no—
102C4⋊C4—942no—
103C4⋊C4—942no—
104C22⋊C4—22no—
105C22⋊C4—942no—
106C22⋊C4—941no—
107C42—941no—
108C42C22×D4711yescharacteristic
109C23—21no—
110C23—1881no—
111Q8—41no—
112Q8—3761no—
113D4—41no—
114D4—1881no—
115D4—1881no—
116D4—1884no—
117C2×C4—21no—
118C2×C4—942no—
119C2×C4—942no—
120C2×C4—3761no—
121C2×C4C2×D18811yescharacteristic
122C2×C4D4×D4712yes—
123C8—42no—
124C8—942no—
125C22—41no—
126C22—42no—
127C22—3761no—
128C22—3762no—
129C22#1309399411yescharacteristic
130C4—21no—
131C4—22no—
132C4—41no—
133C4—1882no—
134C4—1882no—
135C2—81no—
136C2—7521no—
137C2#1568929311yescharacteristic
138C2#1568929712yes—
subgroupG/H
centerC22#13093994
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#329C2
socleC22×C47#120
hypercenter#329D47
hypocenterC47#1657
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
1. #15689873C2semidirect
3. #15689488C2semidirect
4. #15688864C2semidirect
5. C47×#329C2semidirect
74. #329D47semidirect
75. C47#1657semidirect