Finite Group Databasebeta

← #20242695

Subgroups — #20242695

Order 6016.

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

normal subgroups only

This group has 228 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#15689865C211yesmaximal, characteristic
2#15689518C211yesmaximal, characteristic, complemented
3#15689483C212yesmaximal, complemented
4#15688862C212yesmaximal, complemented
5C47×#329C211yesmaximal, characteristic, complemented
6C2×#10625337—21no—
7C2×#10625335—21no—
8#13094024C2211yescharacteristic, complemented
9#13094013—21no—
10#13094012C2212yes—
11#13094010—22no—
12#13093994—22no—
13#13093992—21no—
14#13093949—22no—
15#13093946—22no—
16#13093935C2211yescharacteristic, complemented
17#124×C47C2211yescharacteristic
18#97×C47C2212yescomplemented
19C23×D47—21no—
20C2×Q8×C47D411yescharacteristic
21C2×D4×C47D411yescharacteristic
22C2×C22⋊D47—22no—
23C2×D188—21no—
24C2×D188D412yes—
25C2×Dic94—21no—
26C2×Dic94D412yes—
27C2×C8×C47—22no—
28C22⋊C4×C47—22no—
29C42×C47C2311yescharacteristic
30C22⋊Dic47—21no—
31#10625337—42no—
32#10625335—42no—
33(C2×D47)⋊C4—22no—
34(C2×D47)⋊C4—22no—
35(C2×D47)⋊C4—22no—
36C4⋊Dic47—22no—
37C4×Dic47—21no—
38C2×C47⋊C8—21no—
39C23×C47—21no—
40C22×D47—22no—
41C22×D47—81no—
42C22×D47—82no—
43Q8×C47—41no—
44D4×C47—41no—
45C2×C4×C47—21no—
46C2×C4×C47C2×D411yescharacteristic
47C2×C4×C47C2×D412yes—
48C22⋊D47—82no—
49C2×Dic47—22no—
50C2×Dic47—41no—
51D188—42no—
52D188—81no—
53Dic94—42no—
54Dic94—41no—
55Dic94—41no—
56C8×C47—42no—
57C47⋊C8—22no—
58C22×C47—41no—
59C22×C47—42no—
60C22×C47#12011yescharacteristic
61C2×D47—42no—
62C2×D47—42no—
63C2×D47—42no—
64C2×D47—84no—
65C4×C47—21no—
66C4×C47—22no—
67C4×C47—41no—
68Dic47—42no—
69Dic47—81no—
70#1659—471nomaximal, Sylow
71C2×C47—81no—
72C2×C47#45311yescharacteristic
73C2×C47#45512yes—
74D47—82no—
75H(3,𝔽4)—471no—
76#497—471no—
77#489—472no—
78#329—472no—
79#329D4711yescharacteristic, complemented
80C47#165911yescharacteristic, complemented, Sylow
81C2×Q16—941no—
82C2×SD16—941no—
83C4⋊Q8—471no—
84#124—472no—
85#124—942no—
86#124—941no—
87#124C2×D4711yescharacteristic
88#120—942no—
89#120—941no—
90#103—942no—
91#102—942no—
92#97—471no—
93#97C2×D4712yescomplemented
94C24—941no—
95C2×Q8—472no—
96C2×Q8—941no—
97C2×Q8D18811yescharacteristic
98C2×D4—472no—
99C2×D4—941no—
100C2×D4—942no—
101C2×D4D18811yescharacteristic
102Q16—1882no—
103SD16—1882no—
104C2×C8—22no—
105C2×C8—941no—
106C4⋊C4—942no—
107C22⋊C4—22no—
108C22⋊C4—942no—
109C22⋊C4—941no—
110C22⋊C4—942no—
111C22⋊C4—942no—
112C42—941no—
113C42C22×D4711yescharacteristic
114C23—21no—
115C23—942no—
116C23—3761no—
117C23—3762no—
118Q8—41no—
119Q8—1881no—
120Q8—1881no—
121Q8—1882no—
122D4—41no—
123D4—3761no—
124D4—3762no—
125D4—1882no—
126C2×C4—21no—
127C2×C4—942no—
128C2×C4—1881no—
129C2×C4C2×D18811yescharacteristic
130C2×C4D4×D4712yes—
131C8—42no—
132C8—942no—
133C22—41no—
134C22—42no—
135C22—3764no—
136C22—1882no—
137C22—1882no—
138C22—1882no—
139C22#1309399411yescharacteristic
140C4—21no—
141C4—22no—
142C4—41no—
143C4—3761no—
144C4—1882no—
145C2—81no—
146C2—3762no—
147C2#1568929311yescharacteristic
148C2#1568930212yes—
subgroupG/H
centerC22#13093994
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#329C2
socleC22×C47#120
hypercenter#329D47
hypocenterC47#1659
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. #15689518C2semidirect
3. #15689483C2semidirect
4. #15688862C2semidirect
5. C47×#329C2semidirect
8. #13094024C22semidirect
16. #13093935C22semidirect
18. #97×C47C22semidirect
79. #329D47semidirect
80. C47#1659semidirect
93. #97C2×D47semidirect