Finite Group Databasebeta

← #20242694

Subgroups — #20242694

Order 6016.

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

normal subgroups only

This group has 228 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#15689518C211yesmaximal, characteristic, complemented
2#15689482C212yesmaximal, complemented
3#15688863C212yesmaximal, complemented
4#15688863C211yesmaximal, characteristic, complemented
5C47×H(3,𝔽4)C211yesmaximal, characteristic
6C2×#10625337—21no—
7C2×#10625335—21no—
8#13094024C2211yescharacteristic, complemented
9#13093948—22no—
10#13093945—22no—
11#13093935C2212yescomplemented
12#13093935C2211yescharacteristic, complemented
13#124×C47—22no—
14#124×C47—21no—
15#124×C47C2212yes—
16#124×C47C2211yescharacteristic
17#120×C47—22no—
18#120×C47—21no—
19C24×C47—21no—
20C2×Q8×C47D412yes—
21C2×Q8×C47D411yescharacteristic
22C2×D4×C47—21no—
23C2×D4×C47—22no—
24C2×D4×C47D412yes—
25C2×D4×C47D411yescharacteristic
26C2×Dic94—21no—
27C22⋊C4×C47—22no—
28C22⋊C4×C47—21no—
29C22⋊C4×C47—22no—
30C22⋊C4×C47—22no—
31C22⋊C4×C47—22no—
32C42×C47—21no—
33C42×C47C2311yescharacteristic
34#10625337—42no—
35#10625335—42no—
36C4⋊Dic47—22no—
37C2×C47⋊C8—21no—
38C2×C47⋊C8—22no—
39C23×C47—21no—
40C23×C47—22no—
41C23×C47—81no—
42C23×C47—82no—
43Q8×C47—41no—
44Q8×C47—42no—
45D4×C47—41no—
46D4×C47—42no—
47D4×C47—81no—
48D4×C47—82no—
49C2×C4×C47—21no—
50C2×C4×C47—22no—
51C2×C4×C47C2×D412yes—
52C2×C4×C47C2×D411yescharacteristic
53C2×Dic47—41no—
54Dic94—41no—
55Dic94—41no—
56C47⋊C8—22no—
57C47⋊C8—42no—
58C22×C47—41no—
59C22×C47—42no—
60C22×C47—42no—
61C22×C47—42no—
62C22×C47—42no—
63C22×C47—84no—
64C22×C47#12011yescharacteristic
65C4×C47—21no—
66C4×C47—22no—
67C4×C47—41no—
68C4×C47—42no—
69Dic47—81no—
70#1659—471nomaximal, Sylow
71C2×C47—81no—
72C2×C47—82no—
73C2×C47#45311yescharacteristic
74C2×C47#45512yes—
75H(3,𝔽4)D4711yescharacteristic
76#497—471no—
77#489—472no—
78#329—471no—
79#329—472no—
80C47#165911yescharacteristic, complemented, Sylow
81C2×Q16—941no—
82C2×SD16—941no—
83C4⋊Q8—471no—
84#124—22no—
85#124—21no—
86#124C2×D4712yes—
87#124C2×D4711yescharacteristic
88#120—22no—
89#120—21no—
90#103—942no—
91#102—942no—
92#97—472no—
93#97—471no—
94C24—21no—
95C2×Q8—941no—
96C2×Q8C22⋊D4712yes—
97C2×Q8C22⋊D4711yescharacteristic
98C2×D4—21no—
99C2×D4—22no—
100C2×D4C22⋊D4712yes—
101C2×D4C22⋊D4711yescharacteristic
102Q16—1882no—
103SD16—1882no—
104C2×C8—941no—
105C2×C8—942no—
106C4⋊C4—942no—
107C22⋊C4—22no—
108C22⋊C4—21no—
109C22⋊C4—22no—
110C22⋊C4—22no—
111C22⋊C4—22no—
112C42—21no—
113C42C22×D4711yescharacteristic
114C23—21no—
115C23—22no—
116C23—81no—
117C23—82no—
118Q8—41no—
119Q8—42no—
120Q8—1881no—
121Q8—1881no—
122D4—41no—
123D4—42no—
124D4—81no—
125D4—82no—
126C2×C4—21no—
127C2×C4—22no—
128C2×C4—1881no—
129C2×C4C2×C22⋊D4712yes—
130C2×C4C2×C22⋊D4711yescharacteristic
131C8—942no—
132C8—1882no—
133C22—41no—
134C22—42no—
135C22—42no—
136C22—42no—
137C22—42no—
138C22—84no—
139C22#1309399311yescharacteristic
140C4—21no—
141C4—22no—
142C4—41no—
143C4—42no—
144C4—3761no—
145C2—81no—
146C2—82no—
147C2#1568929111yescharacteristic
148C2#1568930112yes—
subgroupG/H
centerC22#13093993
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×H(3,𝔽4)C2
socleC22×C47#120
hypercenterH(3,𝔽4)D47
hypocenterC47#1659
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #15689518C2semidirect
2. #15689482C2semidirect
3. #15688863C2semidirect
4. #15688863C2semidirect
8. #13094024C22semidirect
11. #13093935C22semidirect
12. #13093935C22semidirect
80. C47#1659semidirect