Finite Group Databasebeta

← C2×#15688939 #20245132

Subgroups — C2×#15688939 #20245132

Order 6016.

216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 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×#13093964C211yesmaximal, characteristic
2C2×#13093960C211yesmaximal, characteristic
3#15688939C214yesmaximal, direct product factor
4C22×Q16×C47C211yesmaximal, characteristic
5C2×#10625329—21no—
6#13093964—21no—
7#13093964C2212yes—
8C2×C47⋊C16—21no—
9#13093960—21no—
10#13093960C2212yes—
11C22×Q8×C47—21no—
12C2×Q16×C47—21no—
13C2×Q16×C47—21no—
14C2×Q16×C47—21no—
15C2×Q16×C47C412yes—
16C2×Q16×C47C412yes—
17C2×Q16×C47C2212yes—
18C22×C8×C47C2211yescharacteristic
19C2×Q8×C47—22no—
20C2×Q8×C47—22no—
21C2×Q8×C47—22no—
22C2×Q8×C47—41no—
23C2×Q8×C47—41no—
24C2×Q8×C47—41no—
25C22×C4×C47—41no—
26C22×C4×C47D411yescharacteristic
27Q16×C47—22no—
28Q16×C47—22no—
29Q16×C47—22no—
30Q16×C47C2×C414yes—
31C2×C8×C47C2×C411yescharacteristic
32C2×C8×C47C2×C411yescharacteristic
33C2×C8×C47D411yescharacteristic
34C2×C8×C47D411yescharacteristic
35C2×C8×C47D411yescharacteristic
36C2×C8×C47C2311yescharacteristic
37#10625329—22no—
38#10625329—41no—
39C2×C47⋊C8—41no—
40C47⋊C16—22no—
41C23×C47SD1611yescharacteristic
42Q8×C47—24no—
43Q8×C47—42no—
44Q8×C47—42no—
45Q8×C47—42no—
46C2×C4×C47—42no—
47C2×C4×C47—42no—
48C2×C4×C47—42no—
49C2×C4×C47C22⋊C411yescharacteristic
50C2×C4×C47C22⋊C411yescharacteristic
51C2×C4×C47D811yescharacteristic
52C2×C4×C47D811yescharacteristic
53C2×C4×C47SD1611yescharacteristic
54C2×C4×C47C2×D411yescharacteristic
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—44no—
65C4×C47#10211yescharacteristic
66C4×C47#10211yescharacteristic
67C4×C47C2×C22⋊C411yescharacteristic
68C4×C47C2×D811yescharacteristic
69C2×#362—471nomaximal, Sylow
70C2×C47—21no—
71C2×C47—21no—
72C2×C47#36212yescomplemented
73C2×C47C2×#10211yescharacteristic
74C22×Q16D4711yescharacteristic
75C2×M32—471no—
76C2×#108—471no—
77#362—474no—
78C47C2×#36211yescharacteristic, complemented, Sylow
79C22×Q8—21no—
80C2×Q16—21no—
81C2×Q16—21no—
82C2×Q16—21no—
83C2×Q16Dic4712yes—
84C2×Q16Dic4712yes—
85C2×Q16C2×D4712yes—
86C2×M16—941no—
87C22×C8C2×D4711yescharacteristic
88M32—472no—
89M32—941no—
90C2×C16—941no—
91#108—472no—
92#108—941no—
93C2×Q8—22no—
94C2×Q8—22no—
95C2×Q8—22no—
96C2×Q8—41no—
97C2×Q8—41no—
98C2×Q8—41no—
99C22×C4—41no—
100C22×C4C22⋊D4711yescharacteristic
101Q16—22no—
102Q16—22no—
103Q16—22no—
104Q16C2×Dic4714yes—
105M16—942no—
106M16—1881no—
107C2×C8—1881no—
108C2×C8C2×Dic4711yescharacteristic
109C2×C8C2×Dic4711yescharacteristic
110C2×C8C22⋊D4711yescharacteristic
111C2×C8C22⋊D4711yescharacteristic
112C2×C8C22⋊D4711yescharacteristic
113C2×C8C22×D4711yescharacteristic
114C16—942no—
115C23#1062533511yescharacteristic
116Q8—24no—
117Q8—42no—
118Q8—42no—
119Q8—42no—
120C2×C4—42no—
121C2×C4—42no—
122C2×C4—42no—
123C2×C4#1062533411yescharacteristic
124C2×C4#1062533411yescharacteristic
125C2×C4#1062533511yescharacteristic
126C2×C4C22⋊Dic4711yescharacteristic
127C2×C4C22⋊Dic4711yescharacteristic
128C2×C4C2×C22⋊D4711yescharacteristic
129C8—1882no—
130C8C22⋊Dic4711yescharacteristic
131C8C22⋊Dic4711yescharacteristic
132C8C22×Dic4711yescharacteristic
133C8C2×C22⋊D4711yescharacteristic
134C22—22no—
135C22#1309394511yescharacteristic
136C22#1309394511yescharacteristic
137C22C2×#1062533511yescharacteristic
138C4—44no—
139C4#1309394511yescharacteristic
140C4#1309394511yescharacteristic
141C4C2×C22⋊Dic4711yescharacteristic
142C4C2×#1062533411yescharacteristic
143C2—21no—
144C2—21no—
145C2#1568893912yesdirect product factor
146C2C2×#1309394511yescharacteristic
subgroupG/H
centerC22#13093945
commutatorC8×C47C22×C4
FrattiniC2×C8C22×D47
FittingC22×Q16×C47C2
socleC22×C47#102
hypercenterC22×Q16D47
hypocenterC47C2×#362
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
3. #15688939C2direct (N × H)
72. C2×C47#362semidirect
78. C47C2×#362semidirect
145. C2#15688939direct (N × H)