Finite Group Databasebeta

← #20243273

Subgroups — #20243273

Order 6016.

224 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 113 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×#13093959C211yesmaximal, characteristic
2#15689159C211yesmaximal, characteristic
3#15689078C211yesmaximal, characteristic
4C2×#13093934C211yesmaximal, characteristic
5#15688884C211yesmaximal, characteristic
6#15688882C211yesmaximal, characteristic
7C47×#405C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10#13093983C2211yescharacteristic
11C2×C4×Dic47C2211yescharacteristic
12#13093959C414yescomplemented
13#13093957C412yescomplemented
14#13093955C412yescomplemented
15#13093934—21no—
16#13093934C414yescomplemented
17C8×Dic47—21no—
18C2×M16×C47C2211yescharacteristic
19C22×C8×C47C2211yescharacteristic
20#117×C47C2211yescharacteristic
21#97×C47—21no—
22C4×C8×C47—21no—
23C22×C4×C47C2311yescharacteristic
24C22×Dic47—21no—
25M16×C47—21no—
26M16×C47C2×C412yes—
27C2×C8×C47—21no—
28C2×C8×C47C2×C412yes—
29C2×C8×C47D411yescharacteristic
30C2×C8×C47D411yescharacteristic
31C2×C8×C47Q812yes—
32C4⋊C4×C47C2×C412yes—
33C22⋊C4×C47—21no—
34C42×C47—21no—
35C22⋊Dic47—21no—
36C4⋊Dic47C2×C412yes—
37C4×Dic47—21no—
38C4×Dic47—21no—
39C4×Dic47C2×C412yes—
40#10625329—21no—
41#10625329C2×C412yes—
42C2×C47⋊C8—21no—
43C2×C47⋊C8C2×C412yes—
44C2×C47⋊C8C2×C411yescharacteristic
45C2×C47⋊C8C2×C411yescharacteristic
46C2×C47⋊C8C2×C412yes—
47C23×C47#4111yescharacteristic
48C2×C4×C47—22no—
49C2×C4×C47C22×C411yescharacteristic
50C2×C4×C47C22×C411yescharacteristic
51C2×C4×C47C22×C411yescharacteristic
52C2×C4×C47C2×D411yescharacteristic
53C2×C4×C47C2×Q811yescharacteristic
54C2×C4×C47#4111yescharacteristic
55C2×Dic47—22no—
56C2×Dic47—22no—
57C2×Dic47—42no—
58C8×C47—22no—
59C8×C47C4⋊C412yes—
60C8×C47C4⋊C412yes—
61C47⋊C8—22no—
62C47⋊C8C4212yes—
63C47⋊C8C4212yes—
64C22×C47—22no—
65C22×C47#11711yescharacteristic
66C22×C47C4×D411yescharacteristic
67C22×C47C4×Q811yescharacteristic
68C4×C47—42no—
69C4×C47C2×C4211yescharacteristic
70C4×C47C2×C4⋊C411yescharacteristic
71C4×C47C4×D411yescharacteristic
72C4×C47C4×Q811yescharacteristic
73Dic47—42no—
74Dic47—42no—
75#1773—471nomaximal, Sylow
76C2×C47—21no—
77C2×C47—21no—
78C2×C47C4×C4⋊C411yescharacteristic
79C2×C47#44412yes—
80C2×#108—471no—
81#427—471no—
82#405—471no—
83#405D4711yescharacteristic
84C2×#97—471no—
85#339—471no—
86#339—471no—
87C47#177311yescharacteristic, complemented, Sylow
88C2×M16—471no—
89C2×M16C2×D4711yescharacteristic
90C22×C8—471no—
91C22×C8C2×D4711yescharacteristic
92#117—471no—
93#117C2×D4711yescharacteristic
94C2×C42—471no—
95#108—474no—
96#107—472no—
97#106—472no—
98#97—21no—
99#97—474no—
100#97—941no—
101C4×C8—21no—
102C4×C8—941no—
103C22×C4—941no—
104C22×C4C22×D4711yescharacteristic
105M16—21no—
106M16—472no—
107M16—941no—
108M16C4×D4712yes—
109C2×C8—21no—
110C2×C8—472no—
111C2×C8—471no—
112C2×C8—471no—
113C2×C8—472no—
114C2×C8—941no—
115C2×C8Dic9412yes—
116C2×C8C4×D4712yes—
117C2×C8C22⋊D4711yescharacteristic
118C2×C8C22⋊D4711yescharacteristic
119C4⋊C4—472no—
120C4⋊C4C4×D4712yes—
121C22⋊C4—21no—
122C22⋊C4—941no—
123C42—21no—
124C42—472no—
125C42—941no—
126C42—941no—
127C23#1062535011yescharacteristic
128C2×C4—22no—
129C2×C4—942no—
130C2×C4—942no—
131C2×C4—1882no—
132C2×C4C2×Dic9411yescharacteristic
133C2×C4C2×C4×D4711yescharacteristic
134C2×C4C2×C4×D4711yescharacteristic
135C2×C4C2×C4×D4711yescharacteristic
136C2×C4#1062535011yescharacteristic
137C2×C4C2×C22⋊D4711yescharacteristic
138C8—22no—
139C8—472no—
140C8—472no—
141C8—942no—
142C8Dic47⋊C412yes—
143C8Dic47⋊C412yes—
144C22—22no—
145C22#1309398111yescharacteristic
146C22C4×C22⋊D4711yescharacteristic
147C22C4×Dic9411yescharacteristic
148C4—42no—
149C4—1882no—
150C4—1882no—
151C4C42×D4711yescharacteristic
152C4C2×Dic47⋊C411yescharacteristic
153C4C4×C22⋊D4711yescharacteristic
154C4C4×Dic9411yescharacteristic
155C2—21no—
156C2—21no—
157C2C4×Dic47⋊C411yescharacteristic
158C2#1568924312yes—
subgroupG/H
centerC2×C4C2×C22⋊D47
commutatorC4×C47C2×C42
FrattiniC22×C4C22×D47
FittingC47×#405C2
socleC22×C47C4×D4
hypercenter#405D47
hypocenterC47#1773
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #405

Complements

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

NH ≅ G/Ntype
12. #13093959C4semidirect
13. #13093957C4semidirect
14. #13093955C4semidirect
16. #13093934C4semidirect
87. C47#1773semidirect