Finite Group Databasebeta

← #20242014

Subgroups — #20242014

Order 6016.

196 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 69 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
1C2×#13094016C211yesmaximal, characteristic
2#15689180C211yesmaximal, characteristic
3#15688864C214yesmaximal, complemented
4C47×#432C211yesmaximal, characteristic
5#13094016—21no—
6#13094016—21no—
7#13094016C412yes—
8#13094016C2212yes—
9C2×C4⋊Dic47C411yescharacteristic
10C2×C4⋊Dic47C411yescharacteristic
11C2×Dic47⋊C4—21no—
12C2×Dic47⋊C4—21no—
13C4⋊(C47⋊C8)—21no—
14C22⋊(C47⋊C8)—21no—
15#13093935C2212yes—
16C2×C42×C47C2211yescharacteristic
17C4⋊C8×C47—21no—
18C22⋊C8×C47—21no—
19#97×C47C2212yes—
20C22×C4×C47C2×C411yescharacteristic
21C22×C4×C47D411yescharacteristic
22C22×C4×C47D411yescharacteristic
23C22×Dic47—21no—
24C22×Dic47—21no—
25C2×C8×C47—22no—
26C42×C47C2×C411yescharacteristic
27C42×C47D411yescharacteristic
28C42×C47D411yescharacteristic
29C42×C47C2311yescharacteristic
30C4⋊Dic47—21no—
31C4⋊Dic47—21no—
32C4⋊Dic47C2×C412yes—
33C4⋊Dic47C2×C412yes—
34Dic47⋊C4—22no—
35Dic47⋊C4—22no—
36Dic47⋊C4—22no—
37Dic47⋊C4—22no—
38C2×C47⋊C8—22no—
39C23×C47C22⋊C411yescharacteristic
40C2×C4×C47—22no—
41C2×C4×C47—41no—
42C2×C4×C47—41no—
43C2×C4×C47C22⋊C411yescharacteristic
44C2×C4×C47C22⋊C411yescharacteristic
45C2×C4×C47C22⋊C411yescharacteristic
46C2×C4×C47C22×C411yescharacteristic
47C2×C4×C47C2×D411yescharacteristic
48C2×C4×C47C2×D411yescharacteristic
49C2×Dic47—22no—
50C2×Dic47—22no—
51C2×Dic47—42no—
52C2×Dic47—42no—
53C8×C47—42no—
54C47⋊C8—42no—
55C22×C47—21no—
56C22×C47—21no—
57C22×C47#10112yes—
58C22×C47C2×C22⋊C411yescharacteristic
59C4×C47—21no—
60C4×C47—21no—
61C4×C47—21no—
62C4×C47—21no—
63C4×C47—21no—
64C4×C47—21no—
65Dic47—42no—
66Dic47—42no—
67#1534—471nomaximal, Sylow
68C2×C47—22no—
69C2×C47C2×#10111yescharacteristic
70C2×C47#42111yescharacteristic
71C2×C47#42111yescharacteristic
72C2×#125—471no—
73#432—471no—
74#432D4711yescharacteristic
75#330—474no—
76C47#153411yescharacteristic, complemented, Sylow
77#125—472no—
78#125—472no—
79#125—941no—
80#125—941no—
81C2×C4⋊C4—471no—
82C2×C4⋊C4—471no—
83C2×C4⋊C4—941no—
84C2×C4⋊C4—941no—
85C2×C42C2×D4711yescharacteristic
86C4⋊C8—21no—
87C4⋊C8—941no—
88C22⋊C8—21no—
89C22⋊C8—941no—
90#97—472no—
91#97C2×D4712yes—
92C22×C4—941no—
93C22×C4—941no—
94C22×C4C4×D4711yescharacteristic
95C22×C4D18811yescharacteristic
96C22×C4C22⋊D4711yescharacteristic
97C2×C8—22no—
98C2×C8—942no—
99C4⋊C4—472no—
100C4⋊C4—472no—
101C4⋊C4—942no—
102C4⋊C4—942no—
103C4⋊C4—941no—
104C4⋊C4—941no—
105C4⋊C4—942no—
106C4⋊C4—942no—
107C42C4×D4711yescharacteristic
108C42D18811yescharacteristic
109C42C22⋊D4711yescharacteristic
110C42C22×D4711yescharacteristic
111C23(C2×D47)⋊C411yescharacteristic
112C2×C4—22no—
113C2×C4—41no—
114C2×C4—41no—
115C2×C4—942no—
116C2×C4—942no—
117C2×C4—1882no—
118C2×C4—1882no—
119C2×C4(C2×D47)⋊C411yescharacteristic
120C2×C4(C2×D47)⋊C411yescharacteristic
121C2×C4(C2×D47)⋊C411yescharacteristic
122C2×C4C2×C4×D4711yescharacteristic
123C2×C4C2×D18811yescharacteristic
124C2×C4C2×C22⋊D4711yescharacteristic
125C8—42no—
126C8—1882no—
127C22—21no—
128C22—21no—
129C22#1309394212yes—
130C22C2×(C2×D47)⋊C411yescharacteristic
131C4—21no—
132C4—21no—
133C4—21no—
134C4—21no—
135C4—21no—
136C4—21no—
137C4—1882no—
138C4—1882no—
139C2—22no—
140C2C2×#1309394211yescharacteristic
141C2#1568913911yescharacteristic
142C2#1568914111yescharacteristic
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×#432C2
socleC22×C47C2×C22⋊C4
hypercenter#432D47
hypocenterC47#1534
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
3. #15688864C2semidirect
76. C47#1534semidirect