Finite Group Databasebeta

← C2×#15688940 #20245133

Subgroups — C2×#15688940 #20245133

Order 6016.

216 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C22×Dic188C211yesmaximal, characteristic
2C2×#13093960C211yesmaximal, characteristic
3#15688940C214yesmaximal, direct product factor
4C2×M32×C47C211yesmaximal, characteristic
5C22×Dic94—21no—
6C2×Dic188—21no—
7C2×Dic188—21no—
8C2×Dic188—21no—
9C2×Dic188C412yes—
10C2×Dic188C412yes—
11C2×Dic188C2212yes—
12C2×#10625329—21no—
13#13093960—21no—
14#13093960C2212yes—
15C22×C8×C47C2211yescharacteristic
16M32×C47—21no—
17M32×C47C2212yes—
18C2×C16×C47—21no—
19C22×C4×C47D411yescharacteristic
20C22×Dic47—41no—
21C2×Dic94—22no—
22C2×Dic94—22no—
23C2×Dic94—22no—
24C2×Dic94—41no—
25C2×Dic94—41no—
26C2×Dic94—41no—
27C2×C8×C47C2×C411yescharacteristic
28C2×C8×C47C2×C411yescharacteristic
29C2×C8×C47D411yescharacteristic
30C2×C8×C47D411yescharacteristic
31C2×C8×C47D411yescharacteristic
32C2×C8×C47C2311yescharacteristic
33#10625329—22no—
34#10625329—41no—
35C2×C47⋊C8—41no—
36Dic188—22no—
37Dic188—22no—
38Dic188—22no—
39Dic188C2×C414yes—
40C16×C47—22no—
41C23×C47SD1611yescharacteristic
42C2×C4×C47C22⋊C411yescharacteristic
43C2×C4×C47C22⋊C411yescharacteristic
44C2×C4×C47D811yescharacteristic
45C2×C4×C47D811yescharacteristic
46C2×C4×C47SD1611yescharacteristic
47C2×C4×C47C2×D411yescharacteristic
48C2×Dic47—42no—
49C2×Dic47—42no—
50C2×Dic47—42no—
51Dic94—24no—
52Dic94—42no—
53Dic94—42no—
54Dic94—42no—
55C8×C47C22⋊C411yescharacteristic
56C8×C47C22⋊C411yescharacteristic
57C8×C47C22×C411yescharacteristic
58C8×C47C2×D411yescharacteristic
59C47⋊C8—42no—
60C22×C47—22no—
61C22×C47#10211yescharacteristic
62C22×C47#10211yescharacteristic
63C22×C47C2×SD1611yescharacteristic
64C4×C47#10211yescharacteristic
65C4×C47#10211yescharacteristic
66C4×C47C2×C22⋊C411yescharacteristic
67C4×C47C2×D811yescharacteristic
68Dic47—44no—
69C2×#362—471nomaximal, Sylow
70C2×C47—21no—
71C2×C47—21no—
72C2×C47#36212yescomplemented
73C2×C47C2×#10211yescharacteristic
74C22×Q16—471no—
75C2×M32D4711yescharacteristic
76C2×#108—471no—
77#362—474no—
78C47C2×#36211yescharacteristic, complemented, Sylow
79C22×Q8—941no—
80C2×Q16—472no—
81C2×Q16—472no—
82C2×Q16—472no—
83C2×Q16—941no—
84C2×Q16—941no—
85C2×Q16—941no—
86C2×M16—941no—
87C22×C8C2×D4711yescharacteristic
88M32—21no—
89M32C2×D4712yes—
90C2×C16—21no—
91#108—472no—
92#108—941no—
93C2×Q8—942no—
94C2×Q8—942no—
95C2×Q8—942no—
96C2×Q8—1881no—
97C2×Q8—1881no—
98C2×Q8—1881no—
99C22×C4—1881no—
100C22×C4D18811yescharacteristic
101Q16—474no—
102Q16—942no—
103Q16—942no—
104Q16—942no—
105M16—942no—
106M16—1881no—
107C2×C8—1881no—
108C2×C8C4×D4711yescharacteristic
109C2×C8C4×D4711yescharacteristic
110C2×C8D18811yescharacteristic
111C2×C8C22⋊D4711yescharacteristic
112C2×C8C22⋊D4711yescharacteristic
113C2×C8C22×D4711yescharacteristic
114C16—22no—
115C23#1062532511yescharacteristic
116Q8—944no—
117Q8—1882no—
118Q8—1882no—
119Q8—1882no—
120C2×C4—1882no—
121C2×C4—1882no—
122C2×C4—1882no—
123C2×C4#1062532511yescharacteristic
124C2×C4D37611yescharacteristic
125C2×C4D37611yescharacteristic
126C2×C4(C2×D47)⋊C411yescharacteristic
127C2×C4(C2×D47)⋊C411yescharacteristic
128C2×C4C2×D18811yescharacteristic
129C8—1882no—
130C8(C2×D47)⋊C411yescharacteristic
131C8(C2×D47)⋊C411yescharacteristic
132C8C2×C4×D4711yescharacteristic
133C8C2×C22⋊D4711yescharacteristic
134C22—22no—
135C22#1309394611yescharacteristic
136C22#1309394611yescharacteristic
137C22C2×#1062532511yescharacteristic
138C4—1884no—
139C4#1309394611yescharacteristic
140C4#1309394611yescharacteristic
141C4C2×(C2×D47)⋊C411yescharacteristic
142C4C2×D37611yescharacteristic
143C2—21no—
144C2—21no—
145C2#1568894012yesdirect product factor
146C2C2×#1309394611yescharacteristic
subgroupG/H
centerC22#13093946
commutatorC8×C47C22×C4
FrattiniC2×C8C22×D47
FittingC2×M32×C47C2
socleC22×C47#102
hypercenterC2×M32D47
hypocenterC47C2×#362
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×M32

Complements

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

NH ≅ G/Ntype
3. #15688940C2direct (N × H)
72. C2×C47#362semidirect
78. C47C2×#362semidirect
145. C2#15688940direct (N × H)