Finite Group Databasebeta

← #20242175

Subgroups — #20242175

Order 6016.

158 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 67 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#15689175C211yesmaximal, characteristic
2#15689174C211yesmaximal, characteristic
3#15689145C211yesmaximal, characteristic
4#15688876C211yesmaximal, characteristic, complemented
5#15688875C211yesmaximal, characteristic, complemented
6#15688873C211yesmaximal, characteristic, complemented
7C47×#334C211yesmaximal, characteristic, complemented
8C2×#10625324—21no—
9C42×D47C2211yescharacteristic
10C4⋊(C47⋊C8)C2211yescharacteristic
11C4⋊(C47⋊C8)C2211yescharacteristic
12Dic47⋊C8—21no—
13Dic47⋊C8C411yescharacteristic
14Dic47⋊C8C411yescharacteristic
15(C2×D47)⋊C8—21no—
16(C2×D47)⋊C8C411yescharacteristic
17(C2×D47)⋊C8C411yescharacteristic
18C4×C47⋊C8C2211yescharacteristic
19C8×Dic47—21no—
20C4⋊C8×C47C2211yescharacteristic
21C4⋊C8×C47C2211yescharacteristic
22C4×C8×C47C2211yescharacteristic
23C2×C4×D47C2×C411yescharacteristic
24C2×C4×D47D411yescharacteristic
25C2×C4×D47Q811yescharacteristic
26C2×C8×C47—21no—
27C2×C8×C47—21no—
28C2×C8×C47C2×C411yescharacteristic
29C2×C8×C47C2×C411yescharacteristic
30C42×C47C2311yescharacteristic
31C4×Dic47C2×C411yescharacteristic
32C4×Dic47D411yescharacteristic
33C4×Dic47Q811yescharacteristic
34C2×C47⋊C8—21no—
35C2×C47⋊C8—21no—
36C2×C47⋊C8C2×C411yescharacteristic
37C2×C47⋊C8C2×C411yescharacteristic
38#10625324—42no—
39C22×D47C4⋊C411yescharacteristic
40C2×C4×C47C22×C411yescharacteristic
41C2×C4×C47C2×D411yescharacteristic
42C2×C4×C47C2×Q811yescharacteristic
43C2×Dic47C4⋊C411yescharacteristic
44C2×Dic47C4⋊C411yescharacteristic
45C2×Dic47C4⋊C411yescharacteristic
46C4×D47—21no—
47C4×D47—21no—
48C4×D47—21no—
49C4×D47—21no—
50C4×D47—22no—
51C8×C47—21no—
52C8×C47—21no—
53C8×C47—41no—
54C8×C47—41no—
55C47⋊C8—21no—
56C47⋊C8—21no—
57C47⋊C8—41no—
58C47⋊C8—41no—
59C22×C47C2×C4⋊C411yescharacteristic
60C2×D47—21no—
61C2×D47—21no—
62C2×D47—21no—
63C4×C47—21no—
64C4×C47#13111yescharacteristic
65C4×C47#13111yescharacteristic
66C4×C47AGL(1,ℤ/8)11yescharacteristic
67C4×C47#13711yescharacteristic
68Dic47—21no—
69Dic47—21no—
70Dic47#10812yes—
71#1574—471nomaximal, Sylow
72C2×C47#42411yescharacteristic
73C2×C47#42811yescharacteristic
74C2×C47C2×#10811yescharacteristic
75D47—41no—
76#431—471no—
77#431—471no—
78#423—471no—
79#335—471no—
80#335—471no—
81#334—471no—
82#334D4711yescharacteristic, complemented
83C47#157411yescharacteristic, complemented, Sylow
84C2×M16—941no—
85C2×C42—471no—
86C4⋊C8—471no—
87C4⋊C8—471no—
88C4⋊C8—471no—
89C4⋊C8—471no—
90C4⋊C8—941no—
91C4⋊C8C2×D4711yescharacteristic
92C4⋊C8C2×D4711yescharacteristic
93C22⋊C8—471no—
94C22⋊C8—471no—
95C22⋊C8—941no—
96C4×C8—471no—
97C4×C8—941no—
98C4×C8C2×D4711yescharacteristic
99C22×C4—471no—
100C22×C4—471no—
101C22×C4—471no—
102M16—1882no—
103C2×C8—21no—
104C2×C8—21no—
105C2×C8—471no—
106C2×C8—471no—
107C2×C8—941no—
108C2×C8—941no—
109C2×C8C4×D4711yescharacteristic
110C2×C8C4×D4711yescharacteristic
111C42—471no—
112C42—471no—
113C42—471no—
114C42C22×D4711yescharacteristic
115C23—471no—
116C2×C4—471no—
117C2×C4—471no—
118C2×C4—471no—
119C2×C4—942no—
120C2×C4—941no—
121C2×C4—941no—
122C2×C4—941no—
123C2×C4—941no—
124C2×C4C2×C4×D4711yescharacteristic
125C2×C4D4×D4711yescharacteristic
126C2×C4Q8×D4711yescharacteristic
127C8—21no—
128C8—21no—
129C8—41no—
130C8—41no—
131C8—941no—
132C8—941no—
133C8—1881no—
134C8—1881no—
135C22—941no—
136C22—941no—
137C22—941no—
138C22C4⋊C4×D4711yescharacteristic
139C4—21no—
140C4—472no—
141C4—941no—
142C4—941no—
143C4#1309403011yescharacteristic
144C4#1309403211yescharacteristic
145C4#1309405111yescharacteristic
146C4#1309405311yescharacteristic
147C2—1881no—
148C2#1568914811yescharacteristic
149C2#1568916211yescharacteristic
150C2#108×D4711yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×#334C2
socleC22×C47C2×C4⋊C4
hypercenter#334D47
hypocenterC47#1574
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C42 ◁ #334

Complements

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

NH ≅ G/Ntype
4. #15688876C2semidirect
5. #15688875C2semidirect
6. #15688873C2semidirect
7. C47×#334C2semidirect
82. #334D47semidirect
83. C47#1574semidirect