Finite Group Databasebeta

← #20242686

Subgroups — #20242686

Order 6016.

206 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 49 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#15689513C211yesmaximal, characteristic
2#15689489C212yesmaximal, complemented
3#15688865C212yesmaximal, complemented
4#15688863C211yesmaximal, characteristic, complemented
5C47×#563C211yesmaximal, characteristic, complemented
6C2×#10625336—21no—
7C2×#10625334—21no—
8#13094021C2211yescharacteristic
9#13093944—22no—
10#13093944—22no—
11#13093935C2212yes—
12#13093935C2211yescharacteristic
13C4⋊Q8×C47—21no—
14#126×C47—22no—
15#125×C47C2212yes—
16#124×C47C2211yescharacteristic
17#123×C47—21no—
18C22⋊Q8×C47—22no—
19C2×Q8×C47—21no—
20C2×Q8×C47D411yescharacteristic
21C2×D4×C47D411yescharacteristic
22C22×C4×C47—21no—
23C2×D188—22no—
24C2×D188—21no—
25C4⋊C4×C47—22no—
26C4⋊C4×C47—22no—
27C4⋊C4×C47—22no—
28C4⋊C4×C47D412yes—
29C4⋊C4×C47D412yes—
30C22⋊C4×C47—22no—
31C22⋊C4×C47—21no—
32C22⋊C4×C47—22no—
33C42×C47—21no—
34C42×C47C2311yescharacteristic
35#10625336—42no—
36#10625334—42no—
37C2×C47⋊C8—21no—
38C2×C47⋊C8—22no—
39C23×C47—21no—
40C22×D47—41no—
41Q8×C47—41no—
42Q8×C47—81no—
43D4×C47—41no—
44C2×C4×C47—22no—
45C2×C4×C47—21no—
46C2×C4×C47—22no—
47C2×C4×C47—81no—
48C2×C4×C47C2×D412yes—
49C2×C4×C47C2×D411yescharacteristic
50D188—41no—
51D188—41no—
52D188—44no—
53C47⋊C8—22no—
54C47⋊C8—42no—
55C22×C47—41no—
56C22×C47—42no—
57C22×C47#12011yescharacteristic
58C2×D47—81no—
59C2×D47—82no—
60C4×C47—21no—
61C4×C47—22no—
62C4×C47—42no—
63C4×C47—41no—
64C4×C47—42no—
65#1657—471nomaximal, Sylow
66C2×C47—81no—
67C2×C47#45311yescharacteristic
68C2×C47#45412yes—
69D47—161no—
70#563D4711yescharacteristic, complemented
71#496—471no—
72#490—472no—
73#330—472no—
74#329—471no—
75C47#165711yescharacteristic, complemented, Sylow
76C2×SD16—941no—
77C2×D8—941no—
78C4⋊Q8—21no—
79#127—471no—
80#126—22no—
81#125C2×D4712yes—
82#124C2×D4711yescharacteristic
83#123—21no—
84C22⋊Q8—22no—
85#102—942no—
86#102—942no—
87#97—472no—
88#97—471no—
89C2×Q8—21no—
90C2×Q8C22⋊D4711yescharacteristic
91C2×D4—942no—
92C2×D4—941no—
93C2×D4C22⋊D4711yescharacteristic
94C22×C4—21no—
95SD16—1882no—
96D8—1882no—
97C2×C8—941no—
98C2×C8—942no—
99C4⋊C4—22no—
100C4⋊C4—22no—
101C4⋊C4—22no—
102C4⋊C4C22⋊D4712yes—
103C4⋊C4C22⋊D4712yes—
104C22⋊C4—22no—
105C22⋊C4—21no—
106C22⋊C4—22no—
107C42—21no—
108C42C22×D4711yescharacteristic
109C23—21no—
110C23—1881no—
111Q8—41no—
112Q8—81no—
113D4—41no—
114D4—1881no—
115D4—1881no—
116D4—1884no—
117C2×C4—22no—
118C2×C4—21no—
119C2×C4—22no—
120C2×C4—81no—
121C2×C4C2×C22⋊D4712yes—
122C2×C4C2×C22⋊D4711yescharacteristic
123C8—942no—
124C8—1882no—
125C22—41no—
126C22—42no—
127C22—3761no—
128C22—3762no—
129C22#1309399311yescharacteristic
130C4—21no—
131C4—22no—
132C4—42no—
133C4—41no—
134C4—42no—
135C2—81no—
136C2—7521no—
137C2#1568929111yescharacteristic
138C2#1568929612yes—
subgroupG/H
centerC22#13093993
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#563C2
socleC22×C47#120
hypercenter#563D47
hypocenterC47#1657
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #563

Complements

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

NH ≅ G/Ntype
2. #15689489C2semidirect
3. #15688865C2semidirect
4. #15688863C2semidirect
5. C47×#563C2semidirect
70. #563D47semidirect
75. C47#1657semidirect