Finite Group Databasebeta

← #20242676

Subgroups — #20242676

Order 6016.

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

normal subgroups only

This group has 262 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, complemented
2#15689510C212yesmaximal, complemented
3#15688863C211yesmaximal, characteristic, complemented
4#15688862C212yesmaximal, complemented
5C47×#496C211yesmaximal, characteristic, complemented
6C2×#10625335—22no—
7C2×#10625334—22no—
8#13094013—21no—
9#13094012C2212yes—
10#13094010—22no—
11#13093994—22no—
12#13093992—21no—
13#13093935C2212yescomplemented
14C2×SD16×C47—21no—
15C2×D8×C47—21no—
16#127×C47C2211yescharacteristic, complemented
17#124×C47C2211yescharacteristic
18#97×C47C2211yescharacteristic, complemented
19C23×D47—21no—
20C2×Q8×C47D411yescharacteristic
21C2×D4×C47—21no—
22C2×D4×C47—22no—
23C2×D4×C47D411yescharacteristic
24C2×C22⋊D47—22no—
25C2×D188—21no—
26C2×D188D412yes—
27C2×Dic94D412yes—
28SD16×C47—42no—
29D8×C47—42no—
30C2×C8×C47—21no—
31C22⋊C4×C47—22no—
32C42×C47C2311yescharacteristic
33C22⋊Dic47—21no—
34#10625335—44no—
35#10625334—44no—
36(C2×D47)⋊C4—22no—
37(C2×D47)⋊C4—22no—
38(C2×D47)⋊C4—22no—
39C4×Dic47—21no—
40C2×C47⋊C8—22no—
41C23×C47—21no—
42C23×C47—41no—
43C22×D47—22no—
44C22×D47—82no—
45C22×D47—81no—
46Q8×C47—41no—
47D4×C47—41no—
48D4×C47—42no—
49D4×C47—42no—
50D4×C47—41no—
51D4×C47—41no—
52C2×C4×C47—21no—
53C2×C4×C47C2×D412yes—
54C2×C4×C47C2×D411yescharacteristic
55C22⋊D47—82no—
56C2×Dic47—22no—
57D188—42no—
58D188—81no—
59Dic94—42no—
60C8×C47—22no—
61C47⋊C8—24no—
62C22×C47—42no—
63C22×C47—41no—
64C22×C47—82no—
65C22×C47—81no—
66C22×C47#12011yescharacteristic
67C2×D47—42no—
68C2×D47—42no—
69C2×D47—42no—
70C2×D47—84no—
71C4×C47—22no—
72C4×C47—21no—
73C4×C47—41no—
74Dic47—42no—
75#1655—471nomaximal, Sylow
76C2×C47—81no—
77C2×C47—161no—
78C2×C47#45312yes—
79C2×C47#45311yescharacteristic
80D47—82no—
81H(3,𝔽4)—471no—
82#496—472no—
83#496D4711yescharacteristic, complemented
84#329—471no—
85#329—472no—
86C47#165511yescharacteristic, complemented, Sylow
87C2×SD16—21no—
88C2×SD16—942no—
89C2×D8—21no—
90C2×D8—942no—
91#127C2×D4711yescharacteristic, complemented
92#124—472no—
93#124—942no—
94#124—941no—
95#124C2×D4711yescharacteristic
96#120—942no—
97#120—941no—
98#97—472no—
99#97C2×D4711yescharacteristic, complemented
100C24—941no—
101C2×Q8—472no—
102C2×Q8C22⋊D4711yescharacteristic
103C2×D4—22no—
104C2×D4—21no—
105C2×D4—472no—
106C2×D4—941no—
107C2×D4—942no—
108C2×D4C22⋊D4711yescharacteristic
109SD16—42no—
110SD16—1884no—
111D8—42no—
112D8—1884no—
113C2×C8—21no—
114C2×C8—942no—
115C22⋊C4—22no—
116C22⋊C4—942no—
117C22⋊C4—941no—
118C22⋊C4—942no—
119C22⋊C4—942no—
120C42—941no—
121C42C22×D4711yescharacteristic
122C23—21no—
123C23—41no—
124C23—942no—
125C23—3762no—
126C23—3761no—
127Q8—41no—
128Q8—1882no—
129D4—41no—
130D4—41no—
131D4—42no—
132D4—41no—
133D4—42no—
134D4—3761no—
135D4—3762no—
136D4—1882no—
137C2×C4—21no—
138C2×C4—942no—
139C2×C4D4×D4712yes—
140C2×C4C2×C22⋊D4711yescharacteristic
141C8—22no—
142C8—944no—
143C22—42no—
144C22—41no—
145C22—82no—
146C22—81no—
147C22—3764no—
148C22—1882no—
149C22—1882no—
150C22—1882no—
151C22#1309399211yescharacteristic
152C4—22no—
153C4—21no—
154C4—41no—
155C4—1882no—
156C2—81no—
157C2—161no—
158C2—3762no—
159C2#1568928912yes—
160C2#1568929011yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#496C2
socleC22×C47#120
hypercenter#496D47
hypocenterC47#1655
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #15689865C2semidirect
2. #15689510C2semidirect
3. #15688863C2semidirect
4. #15688862C2semidirect
5. C47×#496C2semidirect
13. #13093935C22semidirect
16. #127×C47C22semidirect
18. #97×C47C22semidirect
83. #496D47semidirect
86. C47#1655semidirect
91. #127C2×D47semidirect
99. #97C2×D47semidirect