Finite Group Databasebeta

← #20242125

Subgroups — #20242125

Order 6016.

210 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 77 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#15689680C211yesmaximal, characteristic
2#15689147C211yesmaximal, characteristic
3#15688870C212yesmaximal, complemented
4#15688868C212yesmaximal, complemented
5C47×#423C211yesmaximal, characteristic
6C2×#10625329—21no—
7#13094024C2211yescharacteristic
8#13094024C2211yescharacteristic
9#13094016C412yes—
10#13094003—21no—
11#13094003—21no—
12C4×Dic94—21no—
13C4×Dic94—21no—
14#13093983C412yes—
15C4⋊(C47⋊C8)—21no—
16C4⋊(C47⋊C8)C2212yes—
17C2×M16×C47—21no—
18C2×C42×C47C2211yescharacteristic
19C4⋊C8×C47—21no—
20C4⋊C8×C47C2212yes—
21C22×C4×C47C2×C411yescharacteristic
22C22×C4×C47D411yescharacteristic
23C22×C4×C47D411yescharacteristic
24C2×Dic94—21no—
25C2×Dic94—21no—
26M16×C47—42no—
27C2×C8×C47—22no—
28C42×C47C2×C411yescharacteristic
29C42×C47D411yescharacteristic
30C42×C47D411yescharacteristic
31C42×C47C2311yescharacteristic
32C22⋊Dic47—22no—
33C4⋊Dic47—21no—
34C4⋊Dic47—21no—
35C4⋊Dic47C2×C412yes—
36C4⋊Dic47C2×C412yes—
37Dic47⋊C4—22no—
38Dic47⋊C4—22no—
39C4×Dic47—22no—
40#10625329—42no—
41C2×C47⋊C8—22no—
42C23×C47C22⋊C411yescharacteristic
43C2×C4×C47—22no—
44C2×C4×C47—21no—
45C2×C4×C47—21no—
46C2×C4×C47—21no—
47C2×C4×C47—21no—
48C2×C4×C47C22⋊C411yescharacteristic
49C2×C4×C47C22⋊C411yescharacteristic
50C2×C4×C47C22⋊C411yescharacteristic
51C2×C4×C47C22×C411yescharacteristic
52C2×C4×C47C2×D411yescharacteristic
53C2×C4×C47C2×D411yescharacteristic
54C2×Dic47—22no—
55C2×Dic47—22no—
56Dic94—41no—
57Dic94—41no—
58Dic94—41no—
59Dic94—41no—
60C8×C47—42no—
61C47⋊C8—42no—
62C22×C47—21no—
63C22×C47—21no—
64C22×C47—21no—
65C22×C47C2×C22⋊C411yescharacteristic
66C4×C47—21no—
67C4×C47—21no—
68C4×C47—21no—
69C4×C47#10112yes—
70C4×C47AGL(1,ℤ/8)11yescharacteristic
71C4×C47AGL(1,ℤ/8)11yescharacteristic
72C4×C47#13711yescharacteristic
73C4×C47#13711yescharacteristic
74Dic47—42no—
75Dic47—42no—
76#1561—471nomaximal, Sylow
77C2×C47—41no—
78C2×C47C2×#10111yescharacteristic
79C2×C47#41711yescharacteristic
80C2×C47#41711yescharacteristic
81#533—471no—
82#423—471no—
83#423D4711yescharacteristic
84#332—472no—
85#332—472no—
86C47#156111yescharacteristic, complemented, Sylow
87C2×M16—21no—
88C2×M16—941no—
89C4⋊Q8—471no—
90C4⋊Q8—471no—
91#125—472no—
92C22⋊Q8—941no—
93C22⋊Q8—941no—
94C4×Q8—941no—
95C4×Q8—941no—
96#117—472no—
97C2×C42C2×D4711yescharacteristic
98C4⋊C8—21no—
99C4⋊C8—472no—
100C4⋊C8—941no—
101C4⋊C8C2×D4712yes—
102C2×Q8—941no—
103C2×Q8—941no—
104C22×C4C4×D4711yescharacteristic
105C22×C4D18811yescharacteristic
106C22×C4C22⋊D4711yescharacteristic
107M16—42no—
108M16—1882no—
109C2×C8—22no—
110C2×C8—942no—
111C4⋊C4—472no—
112C4⋊C4—472no—
113C4⋊C4—942no—
114C4⋊C4—942no—
115C4⋊C4—941no—
116C4⋊C4—941no—
117C22⋊C4—942no—
118C42—942no—
119C42C4×D4711yescharacteristic
120C42D18811yescharacteristic
121C42C22⋊D4711yescharacteristic
122C42C22×D4711yescharacteristic
123C23(C2×D47)⋊C411yescharacteristic
124Q8—1881no—
125Q8—1881no—
126Q8—1881no—
127Q8—1881no—
128C2×C4—22no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—942no—
134C2×C4—942no—
135C2×C4(C2×D47)⋊C411yescharacteristic
136C2×C4(C2×D47)⋊C411yescharacteristic
137C2×C4(C2×D47)⋊C411yescharacteristic
138C2×C4C2×C4×D4711yescharacteristic
139C2×C4C2×D18811yescharacteristic
140C2×C4C2×C22⋊D4711yescharacteristic
141C8—42no—
142C8—1882no—
143C22—21no—
144C22—21no—
145C22—21no—
146C22C2×(C2×D47)⋊C411yescharacteristic
147C4—21no—
148C4—21no—
149C4—21no—
150C4—1882no—
151C4—1882no—
152C4#1309394212yes—
153C4#1309405011yescharacteristic
154C4#1309405211yescharacteristic
155C4#1309405511yescharacteristic
156C4#1309405711yescharacteristic
157C2—41no—
158C2C2×#1309394211yescharacteristic
159C2#1568912211yescharacteristic
160C2#1568912511yescharacteristic
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×#423C2
socleC22×C47C2×C22⋊C4
hypercenter#423D47
hypocenterC47#1561
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
3. #15688870C2semidirect
4. #15688868C2semidirect
86. C47#1561semidirect