Finite Group Databasebeta

← #20242167

Subgroups — #20242167

Order 6016.

150 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 65 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#15689179C211yesmaximal, characteristic
2#15689175C211yesmaximal, characteristic
3#15689174C211yesmaximal, characteristic
4#15688876C211yesmaximal, characteristic, complemented
5#15688873C211yesmaximal, characteristic, complemented
6#15688873C211yesmaximal, characteristic, complemented
7C47×#335C211yesmaximal, characteristic, complemented
8C42×D47C2211yescharacteristic
9C4⋊(C47⋊C8)C2211yescharacteristic
10C4⋊(C47⋊C8)C2211yescharacteristic
11Dic47⋊C8C411yescharacteristic
12Dic47⋊C8C411yescharacteristic
13(C2×D47)⋊C8—21no—
14(C2×D47)⋊C8—21no—
15(C2×D47)⋊C8C411yescharacteristic
16(C2×D47)⋊C8C411yescharacteristic
17#13093934—21no—
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
38C22×D47C4⋊C411yescharacteristic
39C2×C4×C47C22×C411yescharacteristic
40C2×C4×C47C2×D411yescharacteristic
41C2×C4×C47C2×Q811yescharacteristic
42C2×Dic47C4⋊C411yescharacteristic
43C2×Dic47C4⋊C411yescharacteristic
44C2×Dic47C4⋊C411yescharacteristic
45C4×D47—21no—
46C4×D47—21no—
47C4×D47—21no—
48C4×D47—21no—
49C4×D47—41no—
50C8×C47—21no—
51C8×C47—21no—
52C8×C47—41no—
53C8×C47—41no—
54C47⋊C8—21no—
55C47⋊C8—21no—
56C47⋊C8—41no—
57C47⋊C8—41no—
58C22×C47C2×C4⋊C411yescharacteristic
59C2×D47—21no—
60C2×D47—21no—
61C2×D47—21no—
62C4×C47—21no—
63C4×C47#13111yescharacteristic
64C4×C47#13111yescharacteristic
65C4×C47#13511yescharacteristic
66C4×C47#13511yescharacteristic
67Dic47—21no—
68Dic47—21no—
69Dic47—21no—
70#1572—471nomaximal, Sylow
71C2×C47#42411yescharacteristic
72C2×C47#42711yescharacteristic
73C2×C47#43011yescharacteristic
74D47—41no—
75#432—471no—
76#431—471no—
77#431—471no—
78#335—471no—
79#335D4711yescharacteristic, complemented
80#334—471no—
81#334—471no—
82C47#157211yescharacteristic, complemented, Sylow
83C2×C42—471no—
84C4⋊C8—471no—
85C4⋊C8—471no—
86C4⋊C8—471no—
87C4⋊C8—471no—
88C4⋊C8C2×D4711yescharacteristic
89C4⋊C8C2×D4711yescharacteristic
90C22⋊C8—471no—
91C22⋊C8—471no—
92C22⋊C8—941no—
93C22⋊C8—941no—
94#97—941no—
95C4×C8—471no—
96C4×C8—941no—
97C4×C8C2×D4711yescharacteristic
98C22×C4—471no—
99C22×C4—471no—
100C22×C4—471no—
101C2×C8—21no—
102C2×C8—21no—
103C2×C8—471no—
104C2×C8—471no—
105C2×C8—941no—
106C2×C8—941no—
107C2×C8C4×D4711yescharacteristic
108C2×C8C4×D4711yescharacteristic
109C42—471no—
110C42—471no—
111C42—471no—
112C42C22×D4711yescharacteristic
113C23—471no—
114C2×C4—471no—
115C2×C4—471no—
116C2×C4—471no—
117C2×C4—941no—
118C2×C4—941no—
119C2×C4—941no—
120C2×C4—941no—
121C2×C4—1881no—
122C2×C4C2×C4×D4711yescharacteristic
123C2×C4D4×D4711yescharacteristic
124C2×C4Q8×D4711yescharacteristic
125C8—21no—
126C8—21no—
127C8—41no—
128C8—41no—
129C8—941no—
130C8—941no—
131C8—1881no—
132C8—1881no—
133C22—941no—
134C22—941no—
135C22—941no—
136C22C4⋊C4×D4711yescharacteristic
137C4—21no—
138C4—941no—
139C4—941no—
140C4—941no—
141C4#1309403011yescharacteristic
142C4#1309403211yescharacteristic
143C4#1309404311yescharacteristic
144C4#1309404711yescharacteristic
145C2—1881no—
146C2#1568914811yescharacteristic
147C2#1568916011yescharacteristic
148C2#1568917011yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×#335C2
socleC22×C47C2×C4⋊C4
hypercenter#335D47
hypocenterC47#1572
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C42 ◁ #335

Complements

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

NH ≅ G/Ntype
4. #15688876C2semidirect
5. #15688873C2semidirect
6. #15688873C2semidirect
7. C47×#335C2semidirect
79. #335D47semidirect
82. C47#1572semidirect